Question

Order the steps from first to last that would be used to factor:

3x2−13x−10


(7 points)

Answer 1

1) Compute a·c = 3·(−10) = −30 and find two numbers that multiply to −30 and add to −13: −15 and 2.
2) Split the middle term: 3x^2 −15x + 2x −10.
3) Group: (3x^2 −15x) + (2x −10).
4) Factor each group: 3x(x − 5) + 2(x − 5).
5) Factor out the common binomial: (x − 5)(3x + 2).

So 3x^2 −13x −10 = (x − 5)(3x + 2).