9.2 Multiplying and Factoring
aka: lifeguard vs gcf
Let's start with multiplying(aka:lifeguard)
. . . as before the lifeguard is responsible for saving everyone in
the pool. Let's review:
2
4(a + 3)
2
4xa + 4x3
-5x (x + 2x + 1)
2
2
2
-5x x x + -5x x 2x + -5x x 1
4
4a + 12
2
2
3
-5x - 10x - 5x
2
2
2
4d (d - 3d - 7) + 5d
4x(x - 3) + x(x + 1)
4d x d + 4d x -3d + 4d x -7 + 5d
4xx x + 4xx -3 + xxx + xx1
4d - 12d - 28d + 5d
4x - 12x + x + x
2
2
2
4
2
3
2
2
3
2
3
2
4x +x - 11x
You try:
gcf:
greatest common factor
what is the gcf of 32 and 48?
How do we find a gcf using factors?
find the factors of each term
32: 2 2 2 2 2
48: 2 2 2 2
find the factors they have in common
2 2 2 2
the product of those factors is the gcf
2x2x2x2 = 16
3
Find the gcf of the terms of each polynomial below:
the gcf is the lifeguard -- pull the lifeguard out of the pool,
who's left in the pool?
8x - 4
3
3
2
14x + 7x
4c - 8c + 8 gcf: 4
gcf: 4
divide by 4
divide by 4
4(2x - 1)
4(c - 2c + 2)
3
3
25x - 15x
2
2
gcf: 77x
2
divide by 7x
2
2
7x (2x + 1)
3
2
divide by 5x
8d + 4d + 12d gcf:
4d
divide by 4d
5x (5x - 3)
4d(2d + d + 3)
gcf: 5x
2
2
2
2
2
Factor each polynomial. You try.
3
12n - 8n
3
2
8x - 12x + 4x
4
3
3z - 15z - 9z
3
2
2
16m - 8m + 12m
4
2
6x + 12x
4
3
2
6y + 9y - 27y
9.2day2p501:13-24, 34-39