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.
2. Find two numbers that multiply to −30 and add to b = −13: −15 and 2.
3. Split the middle term: 3x^2 − 15x + 2x − 10.
4. Group terms: (3x^2 − 15x) + (2x − 10).
5. Factor each group: 3x(x − 5) + 2(x − 5).
6. Factor out (x − 5): (3x + 2)(x − 5).

So 3x^2 − 13x − 10 = (3x + 2)(x − 5).