1. Factoring
out the
GCF

2. What does it mean to factor a number?
I can factor the number 12 in different ways…
12 = 1 x 12
12 = 2 x 6
12 = 3 x 4
12 = 2 x 2 x 3
12 = 0.5 x 24
A simple way to think of factoring is to break a “number” down into 2 or more pieces that when multiplied will give you that number back again.

3. Therefore, this is the first factor.
Example #1: Factor.
25x2 + 60x4 – 35x3
= 5x2(
5 + 12x2 – 7x)
Always when asked to factor an algebraic expression, begin by looking for a GCF
Now divide 5x2 into each term of the original expression…
25x2 ÷ 5x2 = 5
60x4 ÷ 5x2 = 12x2
35x3 ÷ 5x2 = 7x
The GCF(25x2, 60x4, 35x3) = 5x2
Therefore, this is the first factor.

4. 24x5y3 – 32x2y4 = 8x2y3( 3x3 – 4y) GCF(24x5y3, 32x2y4) = 8x2y3
Example #2: Factor
24x5y3 – 32x2y4
= 8x2y3(
3x3 – 4y)
GCF(24x5y3, 32x2y4) = 8x2y3

5. Example #3: Factor
12a4b2 – 18a5b + 30a3b3
= 6a3b(
2ab – 3a2 + 5b2)
GCF(12a4b2, 18a5b, 30a3b3) = 6a3b

6. 14x3 – 21x5 + 7x2 = 7x2( 2x – 3x3 + 1) GCF(14x3, 21x5, 7x2) = 7x2
Example #4: Factor
14x3 – 21x5 + 7x2
= 7x2(
2x – 3x3 + 1)
GCF(14x3, 21x5, 7x2) = 7x2

7. Example #5: Factor x

8. Example #6: Factor 3