Question

Can someone please help me factor this equation ASAP?!

Answer 1

p(x)=3x^3-12x

Answer 2

@mathmale

Answer 3

\[p(x)=3x^3-12x\]

Answer 4

... is easier to work with.

Each of the terms on the right side of this equation has 2 quantities in common with the other. What are the 2 common quantities?

Answer 5

Yes, I understand factoring and this is my last question. I'm just a little confused since it has the p(x) and it's a binomial instead of a trinomial. I forget a few steps and I want to be sure of my answer.

Answer 6

Do 3 and 12 have anything in common? If so, what?

Answer 7

3x

Answer 8

Just 3.

Answer 9

Do x^3 and x have anything in common? If so, what?

Answer 10

x

Answer 11

@mathmale

Answer 12

yeap, thus, you take out the common factors
\(\bf 3x^3-12x\implies 3x(x^2-4)\qquad {\color{brown}{ 4=2^2}}\implies 3x(x^2-{\color{brown}{ 2^2}})
\\ \quad \\
\textit{now, recall}\implies \textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad
a^2-b^2 = (a-b)(a+b)\)

and factor it away :)

Answer 13

Summary: 3 and 12 have the common factor 3.
x^3 and x have the common factor x.

3x^3 - 12x have the common factor 3x.

Write your p(x) in factored form, please. Can you take this factoring so far as to have nothing left that can be factored?