Question

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

Answer 1

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)

Answer 2

Answer:

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

Step-by-step 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).