Question

122
course
ap precalculus
segment
33 - polynomial long division (dt
quest
2
due thu, oct 23, 2025
2
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1. $(x^{5}-4x^{4}-4x^{3}-27x^{2}-5x - 35)\div(x^{2}+5)$

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answer
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Explanation:

Step1: Divide the leading term of the dividend by the leading term of the divisor

Divide \(x^{5}\) by \(x^{2}\), we get \(x^{3}\).
Multiply \(x^{3}\) by \((x^{2}+5)\): \(x^{3}(x^{2}+5)=x^{5}+5x^{3}\)
Subtract from the dividend: \((x^{5}-4x^{4}-4x^{3}-27x^{2}-5x - 35)-(x^{5}+5x^{3})=-4x^{4}-9x^{3}-27x^{2}-5x-35\)

Step2: Repeat the process

Divide \(-4x^{4}\) by \(x^{2}\), we get \(-4x^{2}\)
Multiply \(-4x^{2}\) by \((x^{2}+5)\): \(-4x^{2}(x^{2}+5)=-4x^{4}-20x^{2}\)
Subtract: \((-4x^{4}-9x^{3}-27x^{2}-5x-35)-(-4x^{4}-20x^{2})=-9x^{3}-7x^{2}-5x - 35\)

Step3: Continue

Divide \(-9x^{3}\) by \(x^{2}\), we get \(-9x\)
Multiply \(-9x\) by \((x^{2}+5)\): \(-9x(x^{2}+5)=-9x^{3}-45x\)
Subtract: \((-9x^{3}-7x^{2}-5x-35)-(-9x^{3}-45x)=-7x^{2}+40x-35\)

Step4: Final division

Divide \(-7x^{2}\) by \(x^{2}\), we get \(-7\)
Multiply \(-7\) by \((x^{2}+5)\): \(-7(x^{2}+5)=-7x^{2}-35\)
Subtract: \((-7x^{2}+40x-35)-(-7x^{2}-35)=40x\)

Answer:

\(x^{3}-4x^{2}-9x - 7+\frac{40x}{x^{2}+5}\)