Question

The area of a rectangle is (x3 – 5x2 + 3x – 15), and the width of the rectangle is (x2 + 3). If area = length × width, what is the length of the rectangle? x + 5 x – 15 x + 15 x – 5

Answer 1

Answer:

D

Step-by-step explanation:

The area of a rectangle is given by the formula:

$A=lw$

So, we are given that the area is:

$x^3-5x^2+3x-15$

And the width is:

$x^2+3$

And we want to find the length. To do so, first substitute the expressions into the equation:

$x^3-5x^2+3x-15=(x^2+3)l$

Thus, to find the length, divide by (x²+3):

$l=\frac{x^3-5x^2+3x-15}{x^2+3}$

So, factor the numerator:

$x^3-5x^2+3x-15$

From the first two terms, factor out a x^2.

From the third and fourth terms, factor out a 3:

$=x^2(x-5)+3(x-5)$

Combine:

$=(x^2+3)(x-5)$

Putting this back:

$l=\frac{(x^2+3)(x-5)}{x^2+3}$

Cancel:

$l=x-5$

And that's our answer :)

I believe it would be D.