Question

Factoring Trinomials (
Factor each completely.
1) 3p² – 2p - 5

Answer 1

factors (3p - 5) and (p + 1)

Explanation:

The quadratic formula always "works" when you're looking to factor a quadratic expression or equation. Here, the coefficients are a = 3, b = -2 and c = -5. The discriminant is thus b²-4ac, which here is (-2)²-4(3)(-5), or 4+60, or 64. Because this discriminant is positive, we know that the quadratic has two real, unequal roots. These roots are:

-(-2)±√64 2 ± 8

p = ------------------- = --------------- = 10/6 and -1, or 5/3 and -1.

2(3) 6

These roots correspond to the factors (3p - 5) and (p + 1).

Answer 2

3p^2 - 2p - 5
3p^2 -5p+3p-5 (5 times 3 equals 15)
p(3p-5) +1(3p-5)
Answer:
(3p - 5)(p + 1)