Question

completley factor the expression by grouping:
40s^3+45s^2-8s-9

Answer 1

With Factoring by grouping you always want to look at your coefficients and see which ones can go into each other.

You have40, 45, 8 and 9 --- I'm ignoring the signs.

So which one of these go into the other?

45/8 equals a mess, so it's not a good choice but 40/8 does go into completely, you get five. Now check does 9 go into 45? It sure does and it goes in 5 times.

So \[40s^3+45s^2-8s-9\] can break up into
\[8(5s^3-s) + 9(5s^2-1) \] and notice we can pull out an s once more and get
\[8s(5s^2-1)+9(5s^2-1)\]
What do we have in common?
\[(5s^2-1)[8s+9]\]
And we are done.