Solved on Mar 07, 2024

Subtract the two polynomials: $\left(3 x^{5}-2 x^{4}-5\right)-\left(2 x^{4}+x^{2}-10\right)$ .

STEP 1

Assumptions
1. We are given two polynomials: $3 x^{5}-2 x^{4}-5$ and $2 x^{4}+x^{2}-10$ .
2. We need to subtract the second polynomial from the first.

STEP 2

To subtract the second polynomial from the first, we change the sign of each term in the second polynomial and then combine like terms with the first polynomial.
$(3 x^{5}-2 x^{4}-5) - (2 x^{4}+x^{2}-10)$

STEP 3

Change the sign of each term in the second polynomial.
$(3 x^{5}-2 x^{4}-5) - (2 x^{4}+x^{2}-10) = (3 x^{5}-2 x^{4}-5) - 2 x^{4} - x^{2} + 10$

STEP 4

Combine like terms by adding or subtracting the coefficients of the terms with the same degree.
$3 x^{5} + (-2 x^{4} - 2 x^{4}) + (-x^{2}) + (-5 + 10)$

STEP 5

Combine the $x^{4}$ terms.
$-2 x^{4} - 2 x^{4} = -4 x^{4}$

STEP 6

Combine the constant terms.
$-5 + 10 = 5$

STEP 7

Now, write down the resulting polynomial after combining like terms.
$3 x^{5} - 4 x^{4} - x^{2} + 5$
The result of subtracting the second polynomial from the first is $3 x^{5} - 4 x^{4} - x^{2} + 5$ .

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Subtract the two polynomials: $\left(3 x^{5}-2 x^{4}-5\right)-\left(2 x^{4}+x^{2}-10\right)$ .

STEP 1

Assumptions
1. We are given two polynomials: $3 x^{5}-2 x^{4}-5$ and $2 x^{4}+x^{2}-10$ .
2. We need to subtract the second polynomial from the first.

STEP 2

To subtract the second polynomial from the first, we change the sign of each term in the second polynomial and then combine like terms with the first polynomial.
$(3 x^{5}-2 x^{4}-5) - (2 x^{4}+x^{2}-10)$

STEP 3

Change the sign of each term in the second polynomial.
$(3 x^{5}-2 x^{4}-5) - (2 x^{4}+x^{2}-10) = (3 x^{5}-2 x^{4}-5) - 2 x^{4} - x^{2} + 10$

STEP 4

Combine like terms by adding or subtracting the coefficients of the terms with the same degree.
$3 x^{5} + (-2 x^{4} - 2 x^{4}) + (-x^{2}) + (-5 + 10)$

STEP 5

Combine the $x^{4}$ terms.
$-2 x^{4} - 2 x^{4} = -4 x^{4}$

STEP 6

Combine the constant terms.
$-5 + 10 = 5$

STEP 7

Now, write down the resulting polynomial after combining like terms.
$3 x^{5} - 4 x^{4} - x^{2} + 5$
The result of subtracting the second polynomial from the first is $3 x^{5} - 4 x^{4} - x^{2} + 5$ .

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Subtract the two polynomials: (3x5−2x4−5)−(2x4+x2−10)\left(3 x^{5}-2 x^{4}-5\right)-\left(2 x^{4}+x^{2}-10\right)(3x5−2x4−5)−(2x4+x2−10).

STEP 1

Assumptions1. We are given two polynomials: 3x5−2x4−53 x^{5}-2 x^{4}-53x5−2x4−5 and 2x4+x2−102 x^{4}+x^{2}-102x4+x2−10.2. We need to subtract the second polynomial from the first.

STEP 2

To subtract the second polynomial from the first, we change the sign of each term in the second polynomial and then combine like terms with the first polynomial.(3x5−2x4−5)−(2x4+x2−10) (3 x^{5}-2 x^{4}-5) - (2 x^{4}+x^{2}-10) (3x5−2x4−5)−(2x4+x2−10)

STEP 3

Change the sign of each term in the second polynomial.(3x5−2x4−5)−(2x4+x2−10)=(3x5−2x4−5)−2x4−x2+10 (3 x^{5}-2 x^{4}-5) - (2 x^{4}+x^{2}-10) = (3 x^{5}-2 x^{4}-5) - 2 x^{4} - x^{2} + 10 (3x5−2x4−5)−(2x4+x2−10)=(3x5−2x4−5)−2x4−x2+10

STEP 4

Combine like terms by adding or subtracting the coefficients of the terms with the same degree.3x5+(−2x4−2x4)+(−x2)+(−5+10) 3 x^{5} + (-2 x^{4} - 2 x^{4}) + (-x^{2}) + (-5 + 10) 3x5+(−2x4−2x4)+(−x2)+(−5+10)

STEP 5

Combine the x4x^{4}x4 terms.−2x4−2x4=−4x4 -2 x^{4} - 2 x^{4} = -4 x^{4} −2x4−2x4=−4x4

STEP 6

Combine the constant terms.−5+10=5 -5 + 10 = 5 −5+10=5

STEP 7

Now, write down the resulting polynomial after combining like terms.3x5−4x4−x2+5 3 x^{5} - 4 x^{4} - x^{2} + 5 3x5−4x4−x2+5The result of subtracting the second polynomial from the first is 3x5−4x4−x2+53 x^{5} - 4 x^{4} - x^{2} + 53x5−4x4−x2+5.

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Subtract the two polynomials: $\left(3 x^{5}-2 x^{4}-5\right)-\left(2 x^{4}+x^{2}-10\right)$ .

Assumptions
1. We are given two polynomials: $3 x^{5}-2 x^{4}-5$ and $2 x^{4}+x^{2}-10$ .
2. We need to subtract the second polynomial from the first.

To subtract the second polynomial from the first, we change the sign of each term in the second polynomial and then combine like terms with the first polynomial.
$(3 x^{5}-2 x^{4}-5) - (2 x^{4}+x^{2}-10)$

Change the sign of each term in the second polynomial.
$(3 x^{5}-2 x^{4}-5) - (2 x^{4}+x^{2}-10) = (3 x^{5}-2 x^{4}-5) - 2 x^{4} - x^{2} + 10$

Combine like terms by adding or subtracting the coefficients of the terms with the same degree.
$3 x^{5} + (-2 x^{4} - 2 x^{4}) + (-x^{2}) + (-5 + 10)$

Combine the $x^{4}$ terms.
$-2 x^{4} - 2 x^{4} = -4 x^{4}$

Combine the constant terms.
$-5 + 10 = 5$

Now, write down the resulting polynomial after combining like terms.
$3 x^{5} - 4 x^{4} - x^{2} + 5$
The result of subtracting the second polynomial from the first is $3 x^{5} - 4 x^{4} - x^{2} + 5$ .