Write the polynomial in the form p(x) = d(x)q(x) + r(x). (−x^5 + 4x^3 − x) ÷ (x^3 − x^2 + 3)

Answer 1

-x^2 -x + 3

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x^3 - x^2 + 0x + 3 | -x^5 + 0x^4 + 4x^3 + 0x^2 -x + 0

-x^5 + x^4 +0x^3 - 3x^2

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-x^4 + 4x^3 + 3x^2 - x

-x^4 + x^3 +0x^2 - 3x

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3x^3 + 3x^2 + 2x

3x^3 - 3x^2 + 0x + 9

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6x^2 + 2x - 9

Check by multiplying:

(-x^2-x+3)(x^3-x^2+0x+3) =

-x^5 + x^4 + 0x^3 - 3x^2

-x^4 + x^3 + 0x^2 - 3x

3x^3 - 3x^2 + 0x + 9

-x^5 + 4x^3 - 6x^2 - 3x + 9

However , adding the remainder of 6x^2 + 2x - 9 causes the 6x^2 terms to cancel as well as the 9.

Also -3x +2x results in -1x

Therefore, the answer is correct