Question

122
course segment
ap precalculus 33 - polynomial long divi
due thu, oct 23, 2025
3
default gallery

1. (2x^{4}+x^{3}-6x^{2}+2x - 20)÷(2x + 5)

text math set matrix
answer

Explanation:

Step1: Divide the leading terms

Divide \(2x^{4}\) by \(2x\). \(\frac{2x^{4}}{2x}=x^{3}\).
Multiply \((2x + 5)\) by \(x^{3}\): \(2x^{4}+5x^{3}\).
Subtract from the dividend: \((2x^{4}+x^{3}-6x^{2}+2x - 20)-(2x^{4}+5x^{3})=-4x^{3}-6x^{2}+2x-20\).

Step2: Repeat the process

Divide \(-4x^{3}\) by \(2x\). \(\frac{-4x^{3}}{2x}=-2x^{2}\).
Multiply \((2x + 5)\) by \(-2x^{2}\): \(-4x^{3}-10x^{2}\).
Subtract: \((-4x^{3}-6x^{2}+2x-20)-(-4x^{3}-10x^{2}) = 4x^{2}+2x-20\).

Step3: Repeat again

Divide \(4x^{2}\) by \(2x\). \(\frac{4x^{2}}{2x}=2x\).
Multiply \((2x + 5)\) by \(2x\): \(4x^{2}+10x\).
Subtract: \((4x^{2}+2x-20)-(4x^{2}+10x)=-8x-20\).

Step4: Final division

Divide \(-8x\) by \(2x\). \(\frac{-8x}{2x}=-4\).
Multiply \((2x + 5)\) by \(-4\): \(-8x-20\).
Subtract: \((-8x - 20)-(-8x-20)=0\).

Answer:

\(x^{3}-2x^{2}+2x - 4\)