Algebra 1 / Unit 8: Polynomials and Factoring
8.4 Factoring Out the GCF and Grouping
Notes
Factoring rewrites a polynomial as a product. Always look for a greatest common factor (GCF) first.
- $6x^3 + 9x^2 = 3x^2(2x + 3)$.
- Grouping (four terms): factor pairs, then factor out the common binomial. $x^3 + 2x^2 + 5x + 10 = x^2(x + 2) + 5(x + 2) = (x^2 + 5)(x + 2)$.
- Check by multiplying back out.
Practice
Factor $8x^2 - 12x$.
The GCF is $4x$.
Factor $15a^3b + 10a^2b^2$.
GCF: $5$, $a^2$ and $b$.
Factor by grouping: $x^3 - 3x^2 + 4x - 12$.
$x^2(x - 3) + 4(x - 3)$.
Ready for more? Take the Unit 8 test.