FACTOR POLYNOMIALS
Factors are the terms you multiply. The answer is referred to as the product.
Example: Factor 36 completely. This directs you to find the prime factors of 36.
36 = 9 ∙ 4 which then can be factored further to 3 ∙ 3 ∙ 2 ∙ 2. Therefore, the factored answer is
3 ∙ 3 ∙ 2 ∙ 2.
When factoring polynomials you are given the "answer", such as m2 - 12m + 27, and are asked to find the "question" or factors, such as (m - 9)(m - 3).
You will be given several approaches to factor polynomials depending on the number of terms.
FACTOR BY GROUPING
You will take this approach when there are four terms in the polynomial.
1) Group the first two terms and the last two terms.
2) Factor a GCF from the first group and factor a GCF from the second group.
3) Factor a GCF again.
EXAMPLES:
1) Factor 3xy + 6y - 2x - 4.
(3xy + 6y) + (-2x - 4) group first two and last two terms
3y(x + 2) - 2(x + 2) factor GCF from each group.
Note: at the above step, you should get another common factor. This is why grouping works for four terms in a polynomial.
(x + 2) (3y - 2) factor common term again
Note: I omitted the dividing step and did it mentally. If you need to understand how I got from this step, 3y(x + 2) - 2(x + 2), to this step, (x + 2)(3y - 2), please see examples 4-8 above.
2) Factor m3 - 2m + m2 - 2.
(m3 - 2m) + (m2 - 2) group first two and last two terms
m(m2 - 2) + 1(m2 - 2) factor GCF from each group (Note: when
there is no term to factor out, then facto a one)
(m2 - 2) (m + 1) factor common term again
3) Factor 12a3 - 8ab2 - 18a2b + 12b3 .
(12a3 - 8ab2) + (-18a2b + 12b3) group first two and last two terms
4a(3a2 - 2b2) - 6b(3a2 - 2b2) factor GCF from each group
(3a2 - 2b2)(4a - 6b) factor common term again