Question

Can someone please explain factoring by grouping for me?

Answer 1

Let's say you want to factor\[x^3+3x^2-4x-12=0\]
Notice the two terms I put in parenthesis have common factors (in the next equation).

The first one has an x^2 in common, and the second has a -4 in common
\[(x^3+3x^2)+(-4x-12)=0\]

Because of this we can bring those factors outside the parenthesis', So;\[x^2(x+3)-4(x+3)=0\]

Now notice in the last equation that every term is multiplied by (x+3), thuse we can take out an (x+3)

\[(x+3)(x^2-4)=0\]

You can further factor the (x^2+4) to get
\[(x+3)(x+2)(x-2)=0\]

So the solutions are: -3, -2, +2