Question

given the area and width of a rectangle below, what is the length? (1 point) area = 9x^2 - 34x + 21 width = x - 3

Explanation:

Step1: Recall area formula for rectangle

The area formula of a rectangle is $A = l\times w$, where $A$ is the area, $l$ is the length and $w$ is the width. We need to find $l=\frac{A}{w}$. Here, $A = 9x^{2}-34x + 21$ and $w=x - 3$.

Step2: Perform polynomial long - division

We divide the polynomial $9x^{2}-34x + 21$ by $x - 3$.
\[

$$\begin{align*} \frac{9x^{2}-34x + 21}{x - 3}&=\frac{9x^{2}-27x-7x + 21}{x - 3}\\ &=\frac{9x(x - 3)-7(x - 3)}{x - 3}\\ &=\frac{(9x - 7)(x - 3)}{x - 3}\\ &=9x-7 \end{align*}$$

\]

Answer:

$9x - 7$