Question

Factor completely h^3+2h^2-9h-18

(please can someone explain to me the steps and not just the answer)

Answer 1

Step 1: Group this into two groups:

`h^3 + 2h^2-9h-18=(h^3 + 2h^2)+(-9h-18)`

When you do that, be sure to group the "–" into the group with the 9 and make sure there's "+" between the groups.

Step 2: Factor out the GCF from both individual groups:

`(h^3 + 2h^2)+(-9h-18) = h^2 (h+2) -9(h+2)`

Step 3: Notice both groups have that (h+2)? That's a new GCF between the two groups, so factor that out:

`h^2 (h+2) -9(h+2) = (h+2)(h^2-9)`

Step 4: That
`(h^2-9)` piece can be factored further, since it's a difference of squares:

`(h+2)(h^2-9) = (h+2)(h+3)(h-3)`

Now it's factored.