1­5 Factoring by GCF, Grouping and DOTS
Aim: How do we factor a polynomial by GCF, Grouping and D.O.T.S.?
Do Now: Review How to Find the Greatest Common Factor of 2 Numbers
Example of G.C.F. of 2 numbers
Step 1: List all factors
12 ­ 2 * 2 * 3
90 ­ 2 * 3 * 3 * 5
Step 2 : Circle all the pairs of factors both numbers have in common
Step 3: Multiply the numbers together
2 * 3 = 6 therefore 6 is the GCF of 12 and 90
Greatest Common Factor of a Polynomial
2
x (x + 2) = x + 2x
multiplied
2
x + 2x = x (x + 2)
factored
Ex. 1 Factor the polynomial using GCF
a.
(find the GCF of the 2 terms)
b.
Factor by Grouping
(needs to have 4 terms)
Ex. 2
Step 1:
Step 2:
Step 3: Factor the GCF from each group again.
Ex. 3
a.
Factoring the Difference of Squares
A 3rd form of factoring is when we have a difference of two squares.
We call this type D.O.T.S.
Ex. 4
Ex. 5
Ex. 6