Question

WILL GIVE MEDAL The area of a rectangle is given by the expression x^3 + x^2 – 11x – 30. If the length of the rectangle is given by the expression x^2 – x – 6, find the expression that represents the width.

Answer 1

@Miracrown

Answer 2

well if you factorize the area you will get two factors one is the length and the other is the width
and since you have the equation of the length you will easily find the width

Answer 3

or you can simply just divide the area over the length

Answer 4

I come up with B?

A.
x – 5
B.
x + 5
C.
x^2 – 5
D.
x^2 + 5

Answer 5

is the equations in the questions are copied correctly ?

Answer 6

The area of a rectangle is given by the expression x^3 +4 x^2 – 11x – 30. If the length of the rectangle is given by the expression x^2 – x – 6, find the expression that represents the width.

Answer 7

see !!
there is no (4x^2) in the question

Answer 8

so yes its B

Answer 9

haha sorry! Thank you!!

Answer 10

yw

Answer 11

You can do this two ways:

You can use long division and divide

\(x^3 +4 x^2 – 11x – 30\) by \(x^2 – x – 6\).

Since you are given choices, you can also look at it this way.

\(\color{red}{x^3} + 4x^2 - 11x \color{blue}{-30} = (\color{red}{x^2} - x \color{blue}{- 6})(\color{red}{A} + \color{blue}{B})\)

\(x^2 \times A = x^3\). That means \(A = x\)
\(-6 \times B = -30\). That means \(B = 5\).

That means the answer must be \(x + 5\).

Answer 12

makes much more sense! Thank you everyone!