Polynomials

Problem 301

3) (n2+10n+18)÷(n+5)\left(n^{2}+10 n+18\right) \div(n+5)

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Problem 302

Question Watch Video Show Examples
Use the long division method to find the result when 8x310x2+x148 x^{3}-10 x^{2}+x-14 is divided by 4x74 x-7. If there is a remainder, express the result in the form q(x)+r(x)b(x)q(x)+\frac{r(x)}{b(x)}. Answer Attempt 1 out of 2

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Problem 303

Question Watch Video Show Examples
Use the long division method to find the result when x38x2+19x15x^{3}-8 x^{2}+19 x-15 is divided by x3x-3. If there is a remainder, express the result in the form q(x)+r(x)b(x)q(x)+\frac{r(x)}{b(x)}.
Answer Attempt 1 out of 2 Submit Answer

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Problem 304

Find the greatest common factor of 10n410 n^{4} and 7c37 c^{3}. \square

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Problem 305

The function f(x)f(x) is defined below. What is the end behavior of f(x)f(x) ? f(x)=1362x23276x24x5+3920+740x3+2x6f(x)=-1362 x^{2}-3276 x-24 x^{5}+3920+740 x^{3}+2 x^{6}
Answer
as x,yx \rightarrow \infty, y \rightarrow \infty and as x,yx \rightarrow-\infty, y \rightarrow-\infty as x,yx \rightarrow \infty, y \rightarrow \infty and as x,yx \rightarrow-\infty, y \rightarrow \infty as x,yx \rightarrow \infty, y \rightarrow-\infty and as x,yx \rightarrow-\infty, y \rightarrow-\infty as x,yx \rightarrow \infty, y \rightarrow-\infty and as x,yx \rightarrow-\infty, y \rightarrow \infty

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Problem 306

Which expression is equivalent to 5(2t+9)+7t5(2 t+9)+7 t ? 2(5t+9)+7t2(9t+5)+7t9(2t+5)+7t17t+45\begin{array}{l} 2(5 t+9)+7 t \\ 2(9 t+5)+7 t \\ 9(2 t+5)+7 t \\ 17 t+45 \end{array} Submit

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Problem 307

The function f(x)f(x) is defined below. What is the end behavior of f(x)f(x) ? f(x)=5x3+385x+80x2+490f(x)=5 x^{3}+385 x+80 x^{2}+490
Answer
as x,yx \rightarrow \infty, y \rightarrow-\infty and as x,yx \rightarrow-\infty, y \rightarrow-\infty as x,yx \rightarrow \infty, y \rightarrow-\infty and as x,yx \rightarrow-\infty, y \rightarrow \infty as x,yx \rightarrow \infty, y \rightarrow \infty and as x,yx \rightarrow-\infty, y \rightarrow \infty as x,yx \rightarrow \infty, y \rightarrow \infty and as x,yx \rightarrow-\infty, y \rightarrow-\infty

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Problem 308

Which expression is equivalent to 5(8s+5)-5(8 s+5) ? 40s+5-40 s+5 5(5+8s)-5(5+8 s) 5(8s5)8(5s5)\begin{array}{l} 5(8 s-5) \\ 8(5 s-5) \end{array}
Submit

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Problem 309

Question The function f(x)f(x) is defined below. What is the end behavior of f(x)f(x) ? f(x)=5x557602880x+520x2+260x310x4f(x)=-5 x^{5}-5760-2880 x+520 x^{2}+260 x^{3}-10 x^{4}
Answer
as x,f(x)x \rightarrow-\infty, f(x) \rightarrow-\infty and as x,f(x)x \rightarrow \infty, f(x) \rightarrow-\infty as x,f(x)x \rightarrow-\infty, f(x) \rightarrow-\infty and as x,f(x)x \rightarrow \infty, f(x) \rightarrow \infty as x,f(x)x \rightarrow-\infty, f(x) \rightarrow \infty and as x,f(x)x \rightarrow \infty, f(x) \rightarrow \infty as x,f(x)x \rightarrow-\infty, f(x) \rightarrow \infty and as x,f(x)x \rightarrow \infty, f(x) \rightarrow-\infty

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Problem 310

Which expression is equivalent to 7(2g6)\rightarrow 7(2 g-6) ? 7(7g+9g6)42g142g+4214g6\begin{array}{c} -7(-7 g+9 g-6) \\ 42 g-14 \\ 2 g+42 \\ -14 g-6 \end{array} Submit

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Problem 311

The function f(x)f(x) is defined below. What is the end behavior of f(x)f(x) ? f(x)=2304+160x28x31056xf(x)=2304+160 x^{2}-8 x^{3}-1056 x
Answer
as x,yx \rightarrow-\infty, y \rightarrow \infty and as x,yx \rightarrow \infty, y \rightarrow \infty
as x,yx \rightarrow-\infty, y \rightarrow \infty and as x,yx \rightarrow \infty, y \rightarrow-\infty as x,yx \rightarrow-\infty, y \rightarrow-\infty and as x,yx \rightarrow \infty, y \rightarrow-\infty
as x,yx \rightarrow-\infty, y \rightarrow-\infty and as x,yx \rightarrow \infty, y \rightarrow \infty

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Problem 312

The function f(x)f(x) is defined below. What is the end behavior of f(x)f(x) ? f(x)=3x463x2+6x3+12066xf(x)=3 x^{4}-63 x^{2}+6 x^{3}+120-66 x
Answer as x,yx \rightarrow \infty, y \rightarrow-\infty and as x,yx \rightarrow-\infty, y \rightarrow-\infty as x,yx \rightarrow \infty, y \rightarrow-\infty and as x,yx \rightarrow-\infty, y \rightarrow \infty
as x,yx \rightarrow \infty, y \rightarrow \infty and as x,yx \rightarrow-\infty, y \rightarrow-\infty as x,yx \rightarrow \infty, y \rightarrow \infty and as x,yx \rightarrow-\infty, y \rightarrow \infty

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Problem 313

11) 12+x4612+x^{4}-6 when x=8x=8

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Problem 314

Which expression is equivalent to 5(5r6)+4(4r+7)5(5 r-6)+4(-4 r+7) ? 11r29r2\begin{array}{l} -11 r-2 \\ 9 r-2 \end{array} 5(6r+5)+4(4r+7)2r+9\begin{array}{c} 5(-6 r+5)+-4(4 r+7) \\ -2 r+9 \end{array} Submit

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Problem 315

(12) m3+9nm^{3}+9 n when m=4m=4 and n=5n=5

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Problem 316

12 Problem 5
Write a possible equation in factored form for the polynomial P(x)P(x) at the right. (2 points)
Page 5

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Problem 317

Find the polynomial function ff with real coefficients that has the given degree, zeros, and function value.  Degree  Zeros 35,i Function Value \begin{array}{cc} \text { Degree } & \text { Zeros } \\ 3 & 5, i \end{array} \quad \begin{array}{c} \text { Function Value } \\ \\ \end{array}

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Problem 318

7. 3x+2yx+4y3x3 x+2 y-x+4 y-3 x
10. 7x3+3x3-7 x^{3}+3 x^{3}

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Problem 319

14. a22ab5ab+6b2a^{2}-2 a b-5 a b+6 b^{2}
16. c2+2cd9cd+d2c^{2}+2 c d-9 c d+d^{2}
18. 2x+3xy+4y5xy+y2132 x+3 x y+4 y-5 x y+y^{2}-13

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Problem 320

Possible factors  Possible factors ±1,±2,±3,±6,±13,±23\begin{array}{l} \text { Possible factors } \\ \pm 1, \pm 2, \pm 3, \pm 6, \pm \frac{1}{3}, \pm \frac{2}{3} \end{array}
2. Factor fully (show your work). &\checkmark \checkmark \checkmark \& \checkmark \checkmark \checkmark a) f(x)=3x34x217x+6f(x)=3 x^{3}-4 x^{2}-17 x+6 b) f(x)=2x38x2+3x12f(x)=2 x^{3}-8 x^{2}+3 x-12

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Problem 321

c. Justify the statement: 3(n4)2+5n2O(n2)3\left(\frac{n}{4}\right)^{2}+5 n^{2} \in O\left(n^{2}\right).

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Problem 322

14. a22ab5ab+6b2a^{2}-2 a b-5 a b+6 b^{2}
16. c2+2cd9cd+d2c^{2}+2 c d-9 c d+d^{2}
18. 2x+3xy+4y5xy+y2132 x+3 x y+4 y-5 x y+y^{2}-13

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Problem 323

3. Which polynomial function's graph is shown here?
1. f(x)=(x+1)(x+3)(x+4)f(x)=(x+1)(x+3)(x+4)
2. f(x)=(x+1)(x3)(x+4)f(x)=(x+1)(x-3)(x+4)
3. f(x)=(x1)(x+3)(x4)f(x)=(x-1)(x+3)(x-4)
4. f(x)=(x1)(x3)(x4)f(x)=(x-1)(x-3)(x-4)

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Problem 324

Divide. (5x230x+23)÷(x5)\left(5 x^{2}-30 x+23\right) \div(x-5)
Your answer should give the quotient and the remainder.
Quotient: \square
Remainder: \square

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Problem 325

8x(5x+9)=8 x(5 x+9)= \square (Simplify your answer.)

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Problem 326

Find a cubic function f(x)=ax3+bx2+cx+df(x)=a x^{3}+b x^{2}+c x+d that has a local maximum value of 3 at x=3x=-3 and a local minimum value of 0 at x=1x=1. f(x)=f(x)=

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Problem 327

Which expression is equivalent to (z+5)(z24z+6)?(z+5)\left(z^{2}-4 z+6\right) ? (A) z3+5z2+6z+30z^{3}+5 z^{2}+6 z+30 (B) z2+z+11z^{2}+z+11 (C) z3+z214z+30z^{3}+z^{2}-14 z+30 (D) z23z+11z^{2}-3 z+11

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Problem 328

Evaluate when n=4n=-4 [3.1]
43. 5n5 n
44. 172n17-2 n

Name the property illustrated. [3.2, 3.3]
45. 3+a=a+33+a=a+3
46. 9+(b+6)=(9+b)+69+(b+6)=(9+b)+6
47. 8(g+7)=8g+568(g+7)=8 g+56
48. 50=05 \cdot 0=0

Factor each expression using the Distributive Property. [3.4]
49. 5x+255 x+25
50. 7m497 m-49
51. Evaluate: (3+7)6+12÷6(3+7) \cdot 6+12 \div 6 \quad [2.7]
52. Evaluate: (35)2+34(3-5)^{2}+3 \cdot 4 [2.7] A. 62 A. 8 B. 12 B. -4 C. 30 C. 16 D. 47 D. 28 E. none of these E. none of these

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Problem 329

4. The graph of a polynomial function ff is shown. Is the degree of the polynomial even or odd? Explain your reasoning. f(x)(x1)(x3)(x+3)(x+1)f(x)-(x-1)(x-3)(x+3)(x+1) \mid (From Unit 2, Lesson 8.)
5. The polynomial function p(x)=x4+4x37x222x+24p(x)=x^{4}+4 x^{3}-7 x^{2}-22 x+24 has known factors of (x+4)(x+4) and (x1)(x-1). a. Rewrite p(x)p(x) as the product of linear factors. b. Draw a rough sketch of the graph of the function.

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Problem 330

Assignment 4.2: Power Functions and Polynomial Score: 0/6 0/6 answered
Question 1
Find the degree of the term -2 : \square Find the degree of the term 1x41 x^{4} : \square Find the degree of the term 3x7-3 x^{7} : \square Find the degree of the term 6x66 x^{6} : \square Find the degree of the polynomial 2+1x43x7+6x6-2+1 x^{4}-3 x^{7}+6 x^{6} : \square Question Help: DVideo Submit question

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Problem 331

Give a parametric equation representation for each curve. a)y=x5xx(t)=y(t)=\begin{array}{l} a) y=x^{5}-x \\ x(t)=\square \\ y(t)=\square \end{array} b) 9x2+y2=19 x^{2}+y^{2}=1 x(t)=x(t)= \square y(t)=y(t)= \square

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Problem 332

(x) Factor 18z4+24z324z218 z^{4}+24 z^{3}-24 z^{2} completely. \square Submit

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Problem 333

(豨) Factor 8z324z218z-8 z^{3}-24 z^{2}-18 z completely. \square Submit

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Problem 334

b) f25p33f2+7p3f^{2}-5 p^{3}-3 f^{2}+7 p^{3}

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Problem 335

(13a8b+11c)+(7b4c)(8a5c)(13 a-8 b+11 c)+(7 b-4 c)-(8 a-5 c)

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Problem 336

(x.) Factor 2t3+14t2+20t2 t^{3}+14 t^{2}+20 t completely. \square Submit

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Problem 337

Simplify. 3(3y4)4(y+4)3(3 y-4)-4(y+4)

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Problem 338

Find the degree, leading coefficient, and the constant term of the polynomial. f(x)=6x25x5x6+6f(x)=-6 x^{2}-5 x^{5}-x^{6}+6
Degree == \square
Leading Coefficient == \square
Constant Term = \square

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Problem 339

Find all the roots of the polynomial: y=x5+11x36x228x+24y=-x^{5}+11 x^{3}-6 x^{2}-28 x+24

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Problem 340

3. Factor this polynomial expression: 6(2x1)29(y+2)2\sqrt{6(2 x-1)^{2}}-9(y+2)^{2} A. (4x+3y+2)(4x3y+10)(4 x+3 y+2)(4 x-3 y+10) C. (8x+3y2)(8x3y+10)(8 x+3 y-2)(8 x-3 y+10) B. (4x+3y2)(4x3y10)(4 x+3 y-2)(4 x-3 y-10) D. (8x+3y+2)(8x3y10)(8 x+3 y+2)(8 x-3 y-10)

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Problem 341

Points: 0 of 1
Find the zeros of the polynomial function and state the multiplicity of each. f(x)=x411x2+18f(x)=x^{4}-11 x^{2}+18
The smallest zero is \square with multiplicity \square 1. . (Type an exact answer, using radicals as needed.) The smaller middle zero is \square with multiplicity \square \square.

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Problem 342

Points: 0 of 1
Find the zeros of the polynomial function and state the multiplicity of each. f(x)=x411x2+18f(x)=x^{4}-11 x^{2}+18
The smallest zero is -3 with multiplicity 1. (Type an exact answer, using radicals as needed.) The smaller middle zero is 2-\sqrt{2} with multiplicity 1. (Type an exact answer, using radicals as needed.) The larger middle zero is \square with multiplicity \square . (Type an exact answer, using radicals as needed.)

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Problem 343

Watch the video and then solve the problem given below. Click here to watch the video. Find the zeros of the function, and their multiplicities. f(x)=x35x2x+5f(x)=x^{3}-5 x^{2}-x+5
The zeros of the function are x=x= \square (Use a comma to separate answers as needed.)

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Problem 344

Watch the video and then solve the problem given below. Click here to watch the video. Find the zeros of the function, and their multiplicities. f(x)=x35x2x+5f(x)=x^{3}-5 x^{2}-x+5
The zeros of the function are x=1,5,1x=1,5,-1. (Use a comma to separate answers as needed.) Each zero has multiplicity \square

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Problem 345

Factor the following four-term polynomial by grouping. 6x+18+xy+3y6x+18+xy+3y=\begin{array}{r} 6 x+18+x y+3 y \\ 6 x+18+x y+3 y= \end{array} \square (Factor completely.)

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Problem 346

Given that f(x)=x25x36f(x)=x^{2}-5 x-36 and g(x)=x9g(x)=x-9, find f(x)÷g(x)f(x) \div g(x) and express the result as a polynomial in simplest form.

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Problem 347

Simplify. 3w4(3z3w)+6z-3 w-4(3 z-3 w)+6 z

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Problem 348

Simplify. 4w(4x6w)2x-4 w-(4 x-6 w)-2 x

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Problem 349

5. For (2x3+5x2kx+9)÷(x+3)\left(2 x^{3}+5 x^{2}-k x+9\right) \div(x+3), determine the value of kk if the remainder is 6 .

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Problem 350

This is the only question in this section.
Question Watch Vid
Write the following expression as a simplified polynomial in standard form. 3(x+2)2+5(x+2)53(x+2)^{2}+5(x+2)-5

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Problem 351

Find the least common multiple of these two expressions. 6x6v3 and 9x7v5w26 x^{6} v^{3} \text { and } 9 x^{7} v^{5} w^{2}

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Problem 352

x2+7xy+12y28x3y34x2+2xy+y2x2+5xy+4y2\frac{x^{2}+7 x y+12 y^{2}}{8 x^{3}-y^{3}} \cdot \frac{4 x^{2}+2 x y+y^{2}}{x^{2}+5 x y+4 y^{2}}

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Problem 353

tributive property to write an equivalent expression. 9(7r3s+10)9(7 r-3 s+10)

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Problem 354

\#5-6: Let g(x)=x4x37x2+x+6g(x)=x^{4}-x^{3}-7 x^{2}+x+6 a. List all possible rational roots according to the Rational Root Theorem
Use the Factor Theorem and Remainder Theorem in order to factor g(x)g(x).

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Problem 355

Determine whether the function is one-to-one. If so, (a) write an equation for the inverse function in the form y=f1(x)y=f^{-1}(x), (b) graph ff and f1f^{-1} on the same axes, and (c) give the domain and the range of ff and f1f^{-1}. If the function is not one-to-one, say so. f(x)=x31f(x)=x^{3}-1 (a) Write an equation for the inverse function in the form y=f1(x)y=f^{-1}(x). Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice. A. The function f(x)f(x) is one-to-one and f1(x)=f^{-1}(x)= \qquad . (Simplify your answer.) B. The function is not one-to-one.

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Problem 356

MATHEMATICS NOV 2024 GR10P1
QEESTION 1 1.1 Given that R=11xx+2R=\sqrt{\frac{11-x}{x+2}}, where x{3;2;0;1,6;7}x \in\{-3 ;-2 ; 0 ; 1,6 ; 7\}
Choose from the given set of xx values one xx value for which RR will be: 1.1.1. Rational (1) 1.1.2. Irrational (1) 1.1.3. Undefined (1) 1.2 Determine, without using a calculator, two negative integers between which 47-\sqrt{47} lie? (2) 1.3 Factorize the following fully 1.3.1 2y2+6y3xy9x2 y^{2}+6 y-3 x y-9 x (2) 1.3.2. x664x^{6}-64 (3) 1.4 Simplify the following expressions fully 1.4.1 x+46x62x6x2\quad x+4-\frac{6 x-6}{2-x}-\frac{6}{x-2} (5) 1.4.216yx+1.27y+1144yx+132x+y1.4 .2 \quad \frac{16^{y-x+1} .27^{y+1}}{144^{y-x+1} \cdot 3^{2 x+y}} (4) [19]

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Problem 357

Factor the following cubic expression. x31331x^{3}-1331 (x11)(x+11)(x-11)(x+11) (x+11)(x211x+121)(x+11)\left(x^{2}-11 x+121\right) (x11)3(x-11)^{3} (x11)(x2+11x+121)(x-11)\left(x^{2}+11 x+121\right)

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Problem 358

\#7: Factor x33x+2x^{\wedge} 3-3 x+2 completely. (5 Points)

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Problem 359

Given the following polynomial and one factor, find the full factored form. Select THREE answer choices. 2x39x2+x+12;(x4)2 x^{3}-9 x^{2}+x+12 ;(x-4) (2x3)(2 x-3) (2x+3)(2 x+3) (x+4)(x+4) (x+1)(x+1) (x1)(x-1) (x4)(x-4)

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Problem 360

Which method would be appropriate to start to factor the polynomial below? 55x340x255 x^{3}-40 x^{2} Ractor by Grouping Greatest Common Factor Sums of Cubes Synthetic Division Difference of Two Squares AC Method

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Problem 361

Which of the following can be factored with grouping? 8x364x2+x88 x^{3}-64 x^{2}+x-8 9x212x+49 x^{2}-12 x+4 4x294 x^{2}-9 8x3+278 x^{3}+27

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Problem 362

13) 4(8x8)-4(-8 x-8)

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Problem 363

Evalúa x2+2y÷2w+3zx^{2}+2 y \div 2 w+3 z para w=2,x=5,y=8w=2, x=5, y=8 yz=3y z=3

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Problem 364

Simplify. 3(y+3)4(y+5)-3(y+3)-4(y+5)

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Problem 365

Find (fg)(x)(f \circ g)(x). f(x)=x+5g(x)=x2\begin{array}{l} f(x)=x+5 \\ g(x)=x^{2} \end{array}
Write your answer as a polynomial in simplest form. (fg)(x)=(f \circ g)(x)= \square 2 3 4 Submit

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Problem 366

Expand and simplify the expression (5x4)(3x+2)(5 x-4)(3 x+2)

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Problem 367

Expand and fully simplify (x+5)(x+4)2(x+5)(x+4)^{2}

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Problem 368

The volume of the cereal box must be 192in33192 \mathrm{in}^{3}{ }^{3}.
Height: (x+10)(x+10) in.
Length: xx in.
Polynomial equation: x3+6x240x=192x^{3}+6 x^{2}-40 x=192
In the context of this problem, which solutions to the polynomial equation can you eliminate because they do not make sense? \checkmark x=8x=-8 \checkmark x=4x=-4 xx x=6x=6 COMPleti What are the dimensions of the cereal box? The length is \square in., the width is \square \square in. Dons
Solutions: x=8,x=4x=-8, x=-4, and x=6x=6

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Problem 369

rement of the progress bar may be uneven because questions can be worth more or less (inciuc
Factor out the Greatest Common Factor (GCF): 64d524d264 d^{5}-24 d^{2} 8d(8d43d)8 d\left(8 d^{4}-3 d\right) 8d2(8d33)8 d^{2}\left(8 d^{3}-3\right) 8d28d38d238 d^{2} \cdot 8 d^{3}-8 d^{2} \cdot 3 4d(16d46d)4 d\left(16 d^{4}-6 d\right)

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Problem 370

Which equation can be solved by using this system of equations? {y=3x55x3+2x210x+4y=4x4+6x311\left\{\begin{array}{l} y=3 x^{5}-5 x^{3}+2 x^{2}-10 x+4 \\ y=4 x^{4}+6 x^{3}-11 \end{array}\right. 3x55x3+2x210x+4=03 x^{5}-5 x^{3}+2 x^{2}-10 x+4=0 3x55x3+2x210x+4=4x4+6x3113 x^{5}-5 x^{3}+2 x^{2}-10 x+4=4 x^{4}+6 x^{3}-11 3x5+4x4+x3+2x210x7=03 x^{5}+4 x^{4}+x^{3}+2 x^{2}-10 x-7=0 4x4+6x311=04 x^{4}+6 x^{3}-11=0

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Problem 371

231) y=(2x3x2+6x+1)3y=\left(2 x^{3}-x^{2}+6 x+1\right)^{3}

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Problem 372

Expand and fully simplify (4p+3)(2p+5)+6(p+3)(4 p+3)(2 p+5)+6(p+3)

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Problem 373

12 The graph of the function m(x)=x3+3x22x4m(x)=x^{3}+3 x^{2}-2 x-4 has a zero at -1 . what are the other zeros of the function? (A) -2 and 2 (B) -1 and 4 (C) 1±5-1 \pm \sqrt{5} (D) 1±231 \pm 2 \sqrt{3}

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Problem 374

Factor. r281r^{2}-81
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. r281=r^{2}-81= \square (Factor completely.) B. The polynomial is prime.

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Problem 375

Factor. s236s^{2}-36
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. s236=s^{2}-36= \square (Factor completely.) B. The polynomial is prime.

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Problem 376

Complete the expressions and select the missing property.
Write each answer as a number, a variable, or the product of a number and a variable. 7+7u+5=7u++5=7u+\begin{aligned} & 7+7 u+5 \\ = & 7 u+\square+5 \\ = & 7 u+\square \end{aligned} Add

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Problem 377

3. Simplify this expression by combining the like terms. (Show your work below) 3x2+2x2+4y3+8y3 x^{2}+2 x^{2}+4 y-3+8 y

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Problem 378

Use long division to divide. (x3+4x23x16)÷(x3)\left(x^{3}+4 x^{2}-3 x-16\right) \div(x-3)

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Problem 379

Factor out the Greatest Common Factor (GCF): 64d532d264 d^{5}-32 d^{2} 8d(8d44d)8 d\left(8 d^{4}-4 d\right) 32d(2d4d)32 d\left(2 d^{4}-d\right) 32d22d332d232 d^{2} \cdot 2 d^{3}-32 d^{2} 32d2(2d31)32 d^{2}\left(2 d^{3}-1\right)

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Problem 380

The movement of the progress bar moy be uneven because questions Find the error in the calculations below, if there is one:  Line (1):4x3+2x26x+3 Line (2):=2x2(2x+1)3(2x+1) Line (3): =2x2(2x+1)+(3)(2x+1) Line (4):=(2x23)(2x+1)\begin{array}{l} \text { Line }(1): 4 x^{3}+2 x^{2}-6 x+3 \\ \begin{array}{l} \text { Line }(2):=2 x^{2}(2 x+1)-3(2 x+1) \\ \text { Line (3): }=2 x^{2}(2 x+1)+(-3)(2 x+1) \\ \text { Line }(4):=\left(2 x^{2}-3\right)(2 x+1) \end{array} \end{array} There are no errors. The error occurred from line (2) to line (3). The error occurred from line (3) to line (4). The enror occurred from line (1) to line (2).

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Problem 381

Three polynomials are factored below, but some coefficients and constants are missing. A d are integers.  1. x2+2x8=(ax+b)(cx+d)\text { 1. } x^{2}+2 x-8=(a x+b)(c x+d)
2. 2x3+2x224x=2x(ax+b)(cx+d)2 x^{3}+2 x^{2}-24 x=2 x(a x+b)(c x+d)
3. 6x215x9=3(ax+b)(cx+d)6 x^{2}-15 x-9=3(a x+b)(c x+d)

Fill in the table with the missing values of a,b,ca, b, c, and dd. a b c d
1. 1 \begin{tabular}{|l|l|l|l|} \hline 1.2 .2 & 1 & \\ \hline 1 & & -2 & 4 \\ \hline 3. & 1 & 1 & -3 \\ \hline & & & \\ \hline \end{tabular}

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Problem 382

Find the error in the calculations below, if there is one: Line (1): 3y3+9y2+30y-3 y^{3}+9 y^{2}+30 y Line (2): =3y(y23y10)=-3 y\left(y^{2}-3 y-10\right) Line (3): =3y(y25y+2y10)=-3 y\left(y^{2}-5 y+2 y-10\right) Line (4): =3y(y(y5)+2(y5))=-3 y(y(y-5)+2(y-5)) Line (5): =3y(y+2)(y5)=-3 y(y+2)(y-5) There are no errors. The error occurred from line (1) to line (2). The error occurred from line (3) to line (4). The error occurred from line (2) to line (3).

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Problem 383

Solve for x.(5x+6)(3x6)=0x .(5 x+6)(3 x-6)=0 x=65x=\frac{6}{5} or x=2x=-2 x=0x=0 x=65x=\frac{-6}{5} or x=2x=2 x=6x=-6 or x=6x=6

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Problem 384

Factor the expression by grouping: 2x214x+3x212 x^{2}-14 x+3 x-21 (2x+7)(x3)(2 x+7)(x-3) (2x7)(x+3)(2 x-7)(x+3) (2x+3)(x7)(2 x+3)(x-7) (2x3)(x+7)(2 x-3)(x+7)

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Problem 385

e) (3x11)(2x+1)(3 x-11)(2 x+1)

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Problem 386

The following equation is given. Complete parts (a)-(c). x33x24x+12=0x^{3}-3 x^{2}-4 x+12=0 a. List all rational roots that are possible according to the Rational Zero Theorem. ±1,±2,±3,±4,±6,±12\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 12 (Use a comma to separate answers as needed.) b. Use synthetic division to test several possible rational roots in order to identify one actual root.
One rational root of the given equation is \square (Simplify your answer.)

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Problem 387

Factor. 27u327-u^{3}

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Problem 388

Find all roots of the polynomial equation. Use the Rational Zero Theorem, Descartes's Rule of Signs, and possibly the graph of the polynomial function shown by a graphing utility as an aid in obtaining the first root. 2x411x3+27x266x+90=02 x^{4}-11 x^{3}+27 x^{2}-66 x+90=0
The solution set of the equation 2x411x3+27x266x+90=02 x^{4}-11 x^{3}+27 x^{2}-66 x+90=0 is \square (Use a comma to separate answers as needed. Type an exact answer, uling radicals and ii as needed. Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

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Problem 389

6. Factor each express a) x2121x^{2}-121

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Problem 390

Factor the expression x3+3x254xx^{3} + 3x^{2} - 54x.

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Problem 391

11. (x28x+15)÷(x3)\left(x^{2}-8 x+15\right) \div(x-3) x5x-5

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Problem 392

Factor the expression x33x240xx^{3}-3x^{2}-40x.

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Problem 393

movement of the progress bar may be uneven because qu Evaluate the expression 2x2y1+3x02 x^{2}-y^{1}+3 x^{0} for x=4x=4 and y=7y=7. 28 60 97 15

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Problem 394

9. f(x)=4x417x2+4f(x)=4 x^{4}-17 x^{2}+4 \begin{tabular}{|l|l|} \hline zero(s): & yy-intercept: \\ \hline \end{tabular}

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Problem 395

10. For n1n \geq 1, establish that the integer n(7n2+5)n\left(7 n^{2}+5\right) is of the form 6k6 k.
11. If nn is an odd integer, show that n4+4n2+11n^{4}+4 n^{2}+11 is of the form 16k16 k.

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Problem 396

Multiply. (5y4)(7y+5)(5 y-4)(7 y+5)
Simplify your answer.

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Problem 397

Multiply. (43y)(4+3y)(4-3 y)(4+3 y)
Simplify your answer.

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Problem 398

Simplify: 11y2+12y6y28y+5y911 y^{2}+12 y-6 y^{2}-8 y+5 y^{9} 9y2+59 y^{2}+5 5y2+4y+55 y^{2}+4 y+5 5y2+4y+15 y^{2}+4 y+1 5y2+9y5 y^{2}+9 y

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Problem 399

Use Synthetic Division to determine each quotient (and remainder - if necessary). If possible, use the quotients to write the dividend in factored form and list all the zeros. If NOT possible with given divisor, write DNE for all applicable answers. Complete work must be shown for credit! (x45x2+4)÷(x+2)\left(x^{4}-5 x^{2}+4\right) \div(x+2)
Quotient: \square Factored Form: \square Zeros: Select an answer \vee \square

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Problem 400

5. Classify each polynomial as a monomial, binomial, or trinomial. State the degree of the polynomial. 5m25 m^{2} Name: Select an answer  ~ \sim
Degree: \square Add Work
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