Question

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

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.