alg14.ppt - Greatest Common Factor (GCF) The Distributive...

1
Greatest Common Factor (GCF)

The Distributive Property says that:

3y(4y + 3x + 6) = 12y
2
+ 9xy + 18y

In 12y
2
+ 9xy + 18y do you see 3y as the
greatest common factor?

We can reverse the process and say that:

12y
2
+ 9xy + 18y = 3y(4y + 3x + 6)

This is called factoring out the GCF

2
The Undistributive Property?

8x
3
+ 2x
2
+ 4x has a common factor, 2x

So it can be rewritten as 2x(4x
2
+ x + 2)

We undistributed or gathered the 2x

What is the gcf of 2x
3
y
2
+ 6x
2
y
2
+ 8x
2
y
4
?

Write it in factored form

Try p36, #4, 6, 8, 10, and 2

3
Factoring 2
nd
Degree Trinomials

Using the FOIL method

(3x + 4)(x + 2) = 3x
2
+ 6x + 4x + 8 or
3x
2
+ 10x + 8

Factoring is the reverse process

How do we get from
3x
2
+ 10x + 8 to (3x + 4)(x + 2) ?

The product of 3x and x make 3x
2

And 2 x 4 = 8 but what about the 10x?

The 10x is the sum of the cross products
(outers and inners), 6x and 4x

4
Factoring as Trial and Error

2x
2
+ 11x + 12 could factor as:
(2x + 6)(x + 2)
(2x - 6)(x - 2)
(2x + 2)(x + 6)
(2x - 2)(x - 6)
(2x + 4)(x + 3)
(2x - 4)(x - 3)
(2x + 3)(x + 4)
(2x - 3)(x - 4)
+10x
-10x
+14x Cross Products
-14x
+10x
-10x
+11x
-11x