Integrated Math 2 / Unit 2: Polynomials and Factoring
2.3 GCF and Factoring by Grouping
Notes
Factoring rewrites a polynomial as a product. Always look for a greatest common factor (GCF) first.
- $12x^3 - 18x^2 = 6x^2(2x - 3)$. Take the largest number and the lowest power of each shared variable.
- Check by multiplying back out.
- Grouping works on four terms: $x^3 + 2x^2 + 3x + 6 = x^2(x + 2) + 3(x + 2) = (x + 2)(x^2 + 3)$.
- If the two groups share no common binomial, try a different grouping.
Practice
Factor out the GCF: $12x^3 - 18x^2$.
The GCF is $6x^2$. The other choices leave a common factor behind.
Factor $4x^2y + 10xy^2$.
The GCF is $2xy$. Dividing gives $2x$ and $5y$.
Factor by grouping: $x^3 + 2x^2 + 3x + 6$.
$x^2(x + 2) + 3(x + 2) = (x + 2)(x^2 + 3)$.
Ready for more? Take the Unit 2 test.