1. March
6, 2013
Today:
Review all Factoring Methods
Covered
Test Grades Posted Today: V6Math
Quarter Grades Posted Tomorrow:
V6Math
New Factor Method: Difference of
Squares
New Khan Academy Topics(2) for
3/10/13
Class Work

2. This is a good time to step back,
Take a deep breath..
(Quietly)
And review what we've covered thus
far in the factoring unit.

3. Greatest Common
Factor
Example: Find the GCF of each list of numbers.
1) 6, 8 and 46
6=2·3
8=2·2·2
46 = 2 · 23
So the GCF is 2.
2) 144, 256 and 300
144 = 2 · 2 · 2 · 3 · 3
256 = 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2
300 = 2 · 2 · 3 · 5 · 5
So the GCF is 2 · 2 = 4.

4. Greatest Common Factor
Example: Find the GCF of each list of terms.
1) x3 and x7
x3 = x · x · x
x7 = x · x · x · x · x · x · x
So the GCF is x · x · x = x3
2) 6x5 and 4x3
6x5 = 2 · 3 · x · x · x
4x3 = 2 · 2 · x · x · x
So the GCF is 2 · x · x · x = 2x3

5. Greatest Common Factor
Example: Find the GCF of the following list of terms.
a3b2, a2b5 and a4b7
a3b2 = a · a · a · b · b
a2b5 = a · a · b · b · b · b · b
a4b7 = a · a · a · a · b · b · b · b · b · b · b
So the GCF is a · a · b · b = a2b2
Notice that the GCF of terms containing variables
will use the smallest exponent found amongst the
individual terms for each variable.

6. Factor Using GCF
Most factoring using GCF is done with binomials.
Factor using GCF:
1. 32x3 – 4x2 2. 18x2y + 5xy2
Sometimes, factoring using GCF is just the first step.
3. 18x2 – 50 4. x3 – 49x

7. factor by Grouping
When a polynomial has 4 or more terms, grouping
is the factor method used.
Factor: xy + 2x + y + 2
It should be clear that we need to rearrange the
terms since there is nothing that can be factored
from the 3rd & 4th terms.
(xy + y) + (2x + 2) =
y(x + 1) + 2(x + 1) =
(x + 1)(y + 2)

8. factor by Grouping
1. xy – 4x + 3y - 12
2. 2xy - 6x - y + 3
3. 2x3 – x2 – 10x + 5
4. 2x + 18 – 9y – xy

9. Factoring: x 2
+ bx + c
Factor c, using those factors whose sum equals b
1. x2 – 2x – 35 3. x2 + 5x + 1
2. x2 – 7x + 10 4. x2 + x - 2

10. Factoring ax2 + bx + c trinomials
First, multiply ac, then, factor c using those factors
whose sum is equivalent to b. Finally, use grouping
to factor the trinomial
1. 2x2 + 7x + 6 3. 3x2 + 17x + 1
2. 3x2 + 14x - 5 4. 8x2 + 2x - 3
5. 6x2 + 7x - 3

11. Solving Equations by Factoring
Zero Factor Theorem
• If a and b are real numbers and ab =
0, then a = 0 or b = 0.
1. x2 + 6x + 8 = 0 3. 6x2 - 14x = -8
x = -4, x = -2 x = 1, x = 11/3
2. x2 - 25 = 0 4. 4x2 - 4x = 24
x = 5, x = -5 x = -2, x = 3

12. Difference of Two Squares
Another shortcut for factoring a trinomial is when
we want to factor the difference of two squares.
a2 – b2 = (a + b)(a – b)
A binomial is the difference of two squares if:
1.Both terms are squares and
2.The signs of the terms are different.
9x2 – 25y2
– c4 + d4

13. Difference of Two Squares
1. b2 - 49 3. 1 - 16x10 =
(b- 7)(b+ 7) (1 - 4x5)(1 + 4x5)
2. 7g3h2 - 28g5 = 4. x2y2 - 25 =
7g3(h2 - 4g2) = (xy - 5)(xy + 5)
7g3(h - 2g)(h + 2g) 5. 144 - x8 =
(12 - x4)(12 + x4)