# Polynomials : Factoring trinomials of the form ax^2 + bx + c where a is not 1 using the ac-method Quiz

Quiz
*Theme/Title: Factoring trinomials of the form ax^2 + bx + c where a is not 1 using the ac-method
* Description/Instructions
This quiz focuses on factoring trinomials of the form
ax^2 + bx + c where a is not 1. The first step is to factor out any common factor, if any. The next step is to multiply the leading coefficient, a, by the constant, c. The next step is to identify two factors of ac, which when multiplied give ac but when added give b. Then express the middle term, bx, as the sum of these two factors. Next factor the first two terms and factor the last two terms. The final step is to express as the product of two binomials,
(x + p)(x + q).

Example:
3x^2 - 10x - 8
There is no common factor other than 1 so the next step is to multiply the leading coefficient 3 and the constant -8. This gives -24.
The two factors which when multiplied give -24 but when added give -10 are -12 and +2, so express -10x as:
-12x + 2x.
This gives overall
3x^2 - 12x + 2x - 8
Now factor the GCF from the first two terms and then from the last two terms.
3x(x - 4) + 2(x - 4)
(3x + 2)(x - 4)

Group: Algebra Algebra Quizzes
Topic: Polynomials