Question

a rectangle has an area of 45x^2 - 42x - 48 and a width of 5x - 8. what is the length of the rectangle? to find the length of the rectangle, use 45x^2 - 42x - 48 as the and 5x - 8 as the

Explanation:

Step1: Recall area formula

The area formula of a rectangle is $A = l\times w$, where $A$ is area, $l$ is length and $w$ is width. We need to find $l=\frac{A}{w}$. Here $A = 45x^{2}-42x - 48$ and $w=5x - 8$.

Step2: Perform polynomial long - division

We divide the polynomial $45x^{2}-42x - 48$ by $5x - 8$.
\[

$$\begin{align*} \frac{45x^{2}-42x - 48}{5x - 8}&=\frac{45x^{2}-72x+30x - 48}{5x - 8}\\ &=\frac{9x(5x - 8)+6(5x - 8)}{5x - 8}\\ &=\frac{(5x - 8)(9x + 6)}{5x - 8}\\ &=9x+6 \end{align*}$$

\]

Answer:

$9x + 6$