Question

A box has a volume given by the trinomial x^3 + 5x^2 - 24x. What are the possible dimensions of the box? use factoring

Answer 1

\[
x^3 + 5x^2 - 24x
\]What's the greatest common factor?

Answer 2

Of both of the numbers?

Answer 3

Well, right now it is obvious the common factor is \(x\).

Answer 4

What happens when you factor out \(x\)?

Answer 5

Then you'll be left with 5 and 24.

Answer 6

\[
x^3 + 5x^2 - 24x=x(x^2 + 5x- 24)
\]

Answer 7

\[
x^2+5-24=x^2-3x+8x-24=x(x-3)+8(x-3)=(x-3)(x+8)
\]

Answer 8

\[
x^3+5x^2−24x=x(x^2+5x-24)=x(x-3)(x+8)
\]

Answer 9

You should practice factoring if you don't already know how to do it.

Answer 10

Thank you for your help, I just don't really understand factoring.