Factoring Polynomials

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

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

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

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

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

Example 1: Factor 25a2 + 15a GCF =

Example 2: Factor 18x2 - 12x3 GCF =

Example 3: Factor 28a2b + 56abc2 GCF =

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

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

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