Question

# The difference of x^{4}+2x^{2}-3x+7 and another polynomial is x^{3}+x^{2}+x-1. What is the

another polynomial?

## The correct answer is: Hence, another polynomial is x4 - x3 + x2 - 4x + 8.

### Answer:

○ Subtraction of polynomials.

○ Always take like terms together while performing subtraction.

○ In addition to polynomials only terms with the same coefficient are subtracted.

- Step by step explanation:

○ Given:

One polynomial: x^{4}+2x^{2}-3x+7

Difference: x^{3}+x^{2}+x-1.

○ Step 1:

○ Let another polynomial be A.

So,

(x^{4}+2x^{2}-3x+7) – A = (x^{3}+x^{2}+x-1)

A = (x^{4}+2x^{2}-3x+7) - (x^{3}+x^{2}+x-1)

A = x^{4 }+ 2x^{2 }- 3x + 7 - x^{3 }- x^{2 }- x + 1

A = x^{4}- x^{3 }+ 2x^{2}- x^{2 }- 3x - x + 7 + 1

A = x^{4 }- x^{3 }+ x^{2 }- 4x + 8

- Final Answer:

Hence, another polynomial is x^{4 }- x^{3 }+ x^{2 }- 4x + 8.

^{4}+2x

^{2}-3x+7

^{3}+x

^{2}+x-1.

○ Step 1:

○ Let another polynomial be A.

So,

^{4}+2x

^{2}-3x+7) – A = (x

^{3}+x

^{2}+x-1)

^{4}+2x

^{2}-3x+7) - (x

^{3}+x

^{2}+x-1)

^{4 }+ 2x

^{2 }- 3x + 7 - x

^{3 }- x

^{2 }- x + 1

^{4}- x

^{3 }+ 2x

^{2}- x

^{2 }- 3x - x + 7 + 1

^{4 }- x

^{3 }+ x

^{2 }- 4x + 8

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