Question

Explain how to factor the following trinomials forms: x2 + bx + c and ax2 + bx + c. Is there more than one way to factor this? Show your answer using both words and mathematical notation.

Answer 1

Factor x^2 + 5x + 6

C = 6 = 1*6 = 2*3.
Select the pair of factors whose sum equals B which is 5.
We select 2 and 3, because their sum = 5.

Solution: (x+2)(x+3).
The solution can be checked by performing the multiplication and
combining like-terms.

Factor 2x^2 + 11x + 12.
This and the previous example can be done by trial and error, but the process can be tedious and very frustrating.

We'll use the AC Method:
A*C = 2 * 12 = 24 = 3*8 = 4*3.
We select the pair of factors whose sum = B(11). Therfore, we select 3 and 8.

2x^2 + (3x+8x) + 12
Arrange the 4 terms into two factorable binomials:
(2x^2+3x) + (8x+12)
x(2x+3) + 4(2x+3)
(2x+3)(x+4).

I hope this helps.