Quotients and Factoring
5-3Monomial Factors of Polynomials
Overview
Factor out the GCF of all terms as a single monomial.
Key ideas
- Find the GCF of coefficients and of variable parts.
- Divide each term by the GCF; place GCF outside.
- Check by re-distributing.
Worked examples
Example 1
Problem. Factor 6x^2 + 9x.
Solution. 3x(2x + 3)
Example 2
Problem. Factor 4a^3 − 8a^2 + 12a.
Solution. 4a(a^2 − 2a + 3)
Practice
Try each one. Click Show answer when ready.
- 1.
Factor 5x^2 − 10x.
- 2.
Factor 6y^3 + 9y^2.
- 3.
Factor 14m^2 − 21m.
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Factor completely: 6x³y − 9x²y² + 12xy³.
- 2.
Factor completely: 10a²b − 15ab² + 25ab.