Factor the polynomial, please

Hi! I was working on my math homework and became stumped on problem number 22, which is: x^3 + x^2 - 12x

Would you please factor out the polynomial for me...? You don't have to give me the answer, just the first few steps and I'll try to figure it out from there. Thanks!

With this kind of problem, you always want to check to see if you can factor out something that is in common with all THREE terms, first. In this case, you can factor out an "x" because each term has an x in it. This gets you to x(x^2 + x - 12).

Next, we want to leave the x on the outside (that we factored out), and focus on what is inside the parentheses. Here, you have to factor a trinomial. What you have to do is look at what factors of -12 (notice the NEGATIVE), and see which factors multiply to equal -12, but also add to equal positive 1 (the implied coefficient in front of the second term). In this case, it would be 4 and -3. So you can factor the trinomial into the two binomials (x + 4)(x - 3).

Now, bring the x that we factored out earlier back into the answer, and you get x(x + 4)(x - 3).

x^3 + x^2 - 12x

factor x out

x(x^2+x-12)

and factor quadratic trinomial
by finding its roots

x(x^2+x-12)=x(x+4)(x-3)

take out the x
x(x^2+x-12)
do magic X thing
i forgot how to do it, try to Google it