Question

Suppose the area of a rectangle is 1023 +37x2 + 38x + 20 and the length is 2x + 5. What is the width of the rectangle?Width:

Answer 1

Explanation

Let's picture the situation of the exercise:

We're looking for the width of the above rectangle. Recall that the area of a rectangle is given by the following equation:

$A=L\cdot W\leftarrow\begin{cases}A=area, \\ L=\text{length,} \\ W=\text{width.}\end{cases}$

For our rectangle, this equation looks like

$10x^3+37x^2+38x+20=(2x+5)\cdot W\text{.}$

Solving this equation for W, we get

$W=\frac{10x^3+37x^2+38x+20}{2x+5}\text{.}$

Then, the exercise turns out to be a polynomial division. let's do it:

Then,

$\frac{10x^3+37x^2+38x+20}{2x+5}=\text{ Quotient}+\text{ Residue}=(5x^2+6x+4)+0=5x^2+6x+4.$

And Thus,

$W=5x^2+6x+4.$Answer

The width of the given rectangle is

$5x^2+6x+4.$