QuestionFactor the GCF from the polynomial: $25 x^{6}+5 x^{4}+35 x^{3}$ .

Studdy Solution

STEP 1

Assumptions1. The polynomial is $25x^6 +5x^4 +35x^3$ . We need to factor out the Greatest Common Factor (GCF) from this polynomial

STEP 2

First, we need to find the GCF of the coefficients (the numbers in front of the variables). The coefficients are25,5, and35.

STEP 3

The GCF of25,5, and35 is5.

STEP 4

Next, we need to find the GCF of the powers of x. The powers are6,4, and3.

STEP 5

The GCF of,4, and3 is3.

STEP 6

Now that we have the GCF of the coefficients and the powers of x, we can write the GCF of the entire polynomial. The GCF is $5x^3$ .

STEP 7

Now, we need to divide each term of the polynomial by the GCF.

STEP 8

Divide the first term, $25x^6$ , by the GCF, $5x^3$ .
$\frac{25x^6}{5x^3}$

STEP 9

Calculate the result of the division.
$\frac{25x^6}{5x^3} =5x^3$

STEP 10

Divide the second term, $5x^4$ , by the GCF, $5x^3$ .
$\frac{5x^4}{5x^3}$

STEP 11

Calculate the result of the division.
$\frac{5x^4}{5x^3} = x$

STEP 12

Divide the third term, 35x^, by the GCF, 5x^.
\frac{35x^}{5x^}

STEP 13

Calculate the result of the division.
$\frac{35x^3}{5x^3} =7$

STEP 14

Now that we have the results of each division, we can write the polynomial after factoring out the GCF.
$x^3(x^3 + x +7)$ The polynomial $25x^6 +x^4 +35x^3$ factored out by the GCF is $x^3(x^3 + x +7)$ .

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QuestionFactor the GCF from the polynomial: $25 x^{6}+5 x^{4}+35 x^{3}$ .

Studdy Solution

STEP 1

Assumptions1. The polynomial is $25x^6 +5x^4 +35x^3$ . We need to factor out the Greatest Common Factor (GCF) from this polynomial

STEP 2

First, we need to find the GCF of the coefficients (the numbers in front of the variables). The coefficients are25,5, and35.

STEP 3

The GCF of25,5, and35 is5.

STEP 4

Next, we need to find the GCF of the powers of x. The powers are6,4, and3.

STEP 5

The GCF of,4, and3 is3.

STEP 6

Now that we have the GCF of the coefficients and the powers of x, we can write the GCF of the entire polynomial. The GCF is $5x^3$ .

STEP 7

Now, we need to divide each term of the polynomial by the GCF.

STEP 8

Divide the first term, $25x^6$ , by the GCF, $5x^3$ .
$\frac{25x^6}{5x^3}$

STEP 9

Calculate the result of the division.
$\frac{25x^6}{5x^3} =5x^3$

STEP 10

Divide the second term, $5x^4$ , by the GCF, $5x^3$ .
$\frac{5x^4}{5x^3}$

STEP 11

Calculate the result of the division.
$\frac{5x^4}{5x^3} = x$

STEP 12

Divide the third term, 35x^, by the GCF, 5x^.
\frac{35x^}{5x^}

STEP 13

Calculate the result of the division.
$\frac{35x^3}{5x^3} =7$

STEP 14

Now that we have the results of each division, we can write the polynomial after factoring out the GCF.
$x^3(x^3 + x +7)$ The polynomial $25x^6 +x^4 +35x^3$ factored out by the GCF is $x^3(x^3 + x +7)$ .

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QuestionFactor the GCF from the polynomial: 25x6+5x4+35x325 x^{6}+5 x^{4}+35 x^{3}25x6+5x4+35x3.

Studdy Solution

STEP 1

Assumptions1. The polynomial is 25x6+5x4+35x325x^6 +5x^4 +35x^325x6+5x4+35x3 . We need to factor out the Greatest Common Factor (GCF) from this polynomial

STEP 2

First, we need to find the GCF of the coefficients (the numbers in front of the variables). The coefficients are25,5, and35.

STEP 3

The GCF of25,5, and35 is5.

STEP 4

Next, we need to find the GCF of the powers of x. The powers are6,4, and3.

STEP 5

The GCF of,4, and3 is3.

STEP 6

Now that we have the GCF of the coefficients and the powers of x, we can write the GCF of the entire polynomial. The GCF is 5x35x^35x3.

STEP 7

Now, we need to divide each term of the polynomial by the GCF.

STEP 8

Divide the first term, 25x625x^625x6, by the GCF, 5x35x^35x3.25x65x3\frac{25x^6}{5x^3}5x325x6​

STEP 9

Calculate the result of the division.25x65x3=5x3\frac{25x^6}{5x^3} =5x^35x325x6​=5x3

STEP 10

Divide the second term, 5x45x^45x4, by the GCF, 5x35x^35x3.5x45x3\frac{5x^4}{5x^3}5x35x4​

STEP 11

Calculate the result of the division.5x45x3=x\frac{5x^4}{5x^3} = x5x35x4​=x

STEP 12

Divide the third term, 35x^, by the GCF, 5x^.\frac{35x^}{5x^}

STEP 13

Calculate the result of the division.35x35x3=7\frac{35x^3}{5x^3} =75x335x3​=7

STEP 14

Now that we have the results of each division, we can write the polynomial after factoring out the GCF.x3(x3+x+7)x^3(x^3 + x +7)x3(x3+x+7)The polynomial 25x6+x4+35x325x^6 +x^4 +35x^325x6+x4+35x3 factored out by the GCF is x3(x3+x+7)x^3(x^3 + x +7)x3(x3+x+7).

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QuestionFactor the GCF from the polynomial: $25 x^{6}+5 x^{4}+35 x^{3}$ .

Assumptions1. The polynomial is $25x^6 +5x^4 +35x^3$ . We need to factor out the Greatest Common Factor (GCF) from this polynomial

Now that we have the GCF of the coefficients and the powers of x, we can write the GCF of the entire polynomial. The GCF is $5x^3$ .

Divide the first term, $25x^6$ , by the GCF, $5x^3$ .
$\frac{25x^6}{5x^3}$

Calculate the result of the division.
$\frac{25x^6}{5x^3} =5x^3$

Divide the second term, $5x^4$ , by the GCF, $5x^3$ .
$\frac{5x^4}{5x^3}$

Calculate the result of the division.
$\frac{5x^4}{5x^3} = x$

Divide the third term, 35x^, by the GCF, 5x^.
\frac{35x^}{5x^}

Calculate the result of the division.
$\frac{35x^3}{5x^3} =7$

Now that we have the results of each division, we can write the polynomial after factoring out the GCF.
$x^3(x^3 + x +7)$ The polynomial $25x^6 +x^4 +35x^3$ factored out by the GCF is $x^3(x^3 + x +7)$ .