Question

122
course segment
ap precalculus 33 - poly
due thu, oct 23, 2025
4
default gallery

1. $(x^{4}-40x^{2}+144)div(x + 6)$ (t

text math set matrix
answer

Explanation:

Step1: Use polynomial long division

$$\begin{align*} x^{4}-40x^{2}+144&=(x + 6)(x^{3}-6x^{2}-4x^{2}+24x)+144-144\\ &=(x + 6)(x^{3}-6x^{2}-4x^{2}+24x)\\ &=(x + 6)(x^{3}-6x^{2}-4x(x - 6))\\ &=(x + 6)(x^{3}-6x^{2}-4x^{2}+24x)\\ &=(x + 6)(x^{3}-10x^{2}+24x)\\ &=(x + 6)x(x^{2}-10x + 24)\\ &=(x + 6)x(x - 4)(x - 6) \end{align*}$$

Step2: Divide by \((x + 6)\)

When we divide \((x^{4}-40x^{2}+144)\) by \((x + 6)\), using the fact that \(x^{4}-40x^{2}+144=(x + 6)x(x - 4)(x - 6)\), the result is \(x(x - 4)(x - 6)=x^{3}-10x^{2}+24x\)

Answer:

\(x^{3}-10x^{2}+24x\)