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

D on Edge 2021 ;))

Explanation:

Answer 2

D

Explanation:

The area of a rectangle is given by the formula:

`A=\ell w`

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)\ell`

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

`\displaystyle \ell = (x^3-5x^2+3x-15)/(x^2+3)`

We can factor the numerator:

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

From the first two terms, factor out a x².

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:

`\displaystyle \ell = ((x^2+3)(x-5))/(x^2+3)`

Cancel:

`\ell =x-5`

Hence, our answer is D.