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

1. Factor: x^2 - 2x - 3.

C = -3 = 1*(-3) = -1*3.
Select the pair whose algebraic sum = -2(1,and-3).
(x+1)(x-3).
The above method works best when the coefficient of x^2 is 1.

2. Factor: 2x^2 + x - 6.
The AC method should be used when the
coefficient of x^2 is not 1:

A*C=2*(-6) = -12 = -1*12 = -2*6 = -3*4.
Use the pair of factors whose algebraic
sum = B(1):
2x^2 + (-3x+4x) - 6.
Arrange the 4 terms to form 2
factorable binomials:
(2x^2+4x) + (-3x-6)
Factor each binomial:
2x(x+2) + -3(x+2)
(x+2)(2x-3).

These 2 methods take all of the guess work out of factoring.