15x^3-9x^2-6x

Question

Can someone please show me how to factor completely.. trying to learn how to do factoring

Answer 1

Usually factoring by grouping is useful when patterns jump out at you:

x^3 + 3x^2 - 6x - 18

you can see x(x^2-6) + 3(x^2-6)

In your problem, that's not likely, so grouping is not a useful method. Instead, factor out the 3x to get

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

Now, if you want to use grouping, you have to play around a bit:

5x^2-3x-2 = 5x^2-5x + 2x-2
= 5x(x-1) + 2(x-1)
= (5x+2)(x-1)

Again, picking up on how to group is a skill learned through experience. Just buckle down and do a few hundred exercises, and you too will be proficient!