1. Factoring
Polynomials

2. Greatest Common Factor (GCF)
A greatest common factor is the biggest monomial that can be divided out of two or more monomials.

3. Try it with just constants.
6 and 18
15 and 24
9 and 21

4. Now, variables.
x and x2
x3 and x7
x2 and y2

5. Put it all together!
25a2 and 15a
18x2 and 12x3
28a2b and 56abc2

6. Factoring!
Step 1) Find the GCF. Step 2) Divide each term by the GCF. Step 3) Check your work by distributing.

7. Example 1: Factor 25a2 + 15a
GCF =

8. Example 2: Factor 18x2 - 12x3
GCF =

9. Example 3: Factor 28a2b + 56abc2
GCF =

10. Example 4: Factor 20x2 - 24xy x(20 – 24y) 2x(10x – 12y) 4(5x2 – 6xy)

11. Example 5: Factor 28a2 + 21b - 35b2c2
GCF =

12. Example 6: Factor 16xy2 - 24y2z + 40y2
2y2(8x – 12z + 20)
4y2(4x – 6z + 10)
8y2(2x - 3z + 5)
8xy2z(2 – 3 + 5)