Question

Is the grouping method to factor 5x^3+15x^2-2x-6

Answer 1

`(x+3)(5x^2-2)`

Explanation:

`5x^3+15x^2-2x-6`

The grouping method means you are going to group some terms together and then factor what you can out of each pair to hopefully make the expression you started with factorable.

Let's try it.

`5x^3+15x^2+-2x-6`

I like to insert a + in front of the last two terms if it isn't already one. I think it makes it less confusing.

I'm going to group the first two terms together and I'm going to group the last two terms together like so:

`(5x^3+15x^2)+(-2x-6)`

Now I'm going to factor what I can out of each pairing.

`5x^2(x+3)+-2(x+3)`

(*I always factor out negative number if the first term in the second pair has a negative on it.)

Now notice in each pairing, there is a common factor of (x+3) so I can factor that out.

The expression then becomes:

`(x+3)(5x^2-2)`