FACTORING REVIEW
1. GCF: Greatest Common Factorthis should ALWAYS be your first thought!
3x2 – 9x
-5a2b4 + 20ab3 – 15a4b2
4x(3x – 2b) + 5(3x – 2b)
2. SIMPLE TRINOMIALS:
3 terms
1st term is a single (letter)2—coefficient = 1
last term is not a perfect square
2nd term is the “sum” of the factors of the last term, which is the “product”
x2 + 7x + 12
y2 – 2y – 8
x2 – 8x + 15
4x2 + 12x – 40
3. PERFECT SQUARE TRINOMIAL:
3 terms
1st term and last term are perfect squares
last term is always positive
middle term is the product of the first and last terms of binomial times 2
factors to 2 identical factors (binomial)
1st term may have a coefficient, but it must be a perfect square
x2 + 6x + 9
4x2 + 12x + 9
18x2 – 12x + 2
4. DIFFERENCE OF SQUARES:
2 terms
ALWAYS subtraction of 2 perfect squares
factors are identical BUT opposite
w2 – 81
9z2 – 16
2x3 – 72x
2a4 – 32
5. COMPLEX TRINOMIALS:
3 terms
1st term has a coefficient which cannot be removed by factoring
both 1st and last terms are NOT perfect squares
3x2 + 7x – 20
2y2 – 7y + 5
6. FACTOR BY GROUPING:
more than 3 terms
group terms that have a common factor
wx + wy + xz + yz
5m2t – 10m2 + t2 – 2t
x2 + x – xy – y
xy + 12 + 4x + 3y
2x2 + 6y + 4x + 3xy