Question

Factor the following problem completely. First, factor out the greatest common factor, and then factor the remaining trinomial:

2r^3 + 8r^2 - 24r

Answer 1

\[ 2r^3 + 8r^2 - 24r = 2r(r^2 + 4r - 12) = 2r(r + 6)(r - 2) \]

Answer 2

I guessed the last step, but it is possible to do it without guessing. Solve \(r^2 + 4r - 12 = 0\) to get two roots \(r_1\) and \(r_2\). \(r^2 + 4r - 12\) may then be factored as \((r - r_1)(r - r_2)\).

Answer 3

Correct! Thank you, next question.