Question

the area of a rectangle is $(x^{4}+4x^{3}+3x^{2}-4x - 4)$, and the length of the rectangle is $(x^{3}+5x^{2}+8x + 4)$. if area = length × width, what is the width of the rectangle?
$x + 1$
$x - 9$
$x + 4$
$x - 1$

Explanation:

Step1: Set up the division

Since \( \text{Area}=\text{Length}\times\text{Width}\), then \( \text{Width}=\frac{\text{Area}}{\text{Length}}\). So we need to divide \(x^{4}+4x^{3}+3x^{2}-4x - 4\) by \(x^{3}+5x^{2}+8x + 4\).

Step2: Polynomial long - division

$$
LATEXBLOCK0
$$

When we use polynomial long - division:

$$
LATEXBLOCK1
$$

Answer:

\(x - 1\) (Option D)