Find the GCF of each pair of monomials:1. 3x2, 9x3

2. p2q3, p3q2

3. 27ab2, 48bc Factor:4. 10b + 25b4

5. -35x3y5 + 7x2y6. 4a + 8b + 12 Solve.7. 19x = 768. -2x + 18 = -72 – 5x9. x – 4 = 5

3

3x²p²q² 3b

5b(2 + 5b³)7x²y(-5xy4 +

1)4(a + 2b + 3)

x = 4 x = -30

x = 27

8

-24

-5

-18

312

-44

7

2

-4-36-83 11

6

Diamond PuzzlePlease complete the following puzzles.

 

Notes 9.2 Factoring using the AC (diamond) method

Coefficients are the numbers located directly in front of the variables. For example, in 2x3, 2 is the coefficient. A trinomial is a three term polynomial. The coefficients in a trinomial have special names. The names of coefficients:

1x2 + 5x - 6

a b c We are going to factor using the AC (diamond) method. This method only works on trinomials in the form above (a, b, c) or binomials in the form (a, c) such as x2 – 4.

 

a•c

b

1 •(-6)

5 5

-6

6 -1

To use the AC method, complete the following four steps. Step 1: Complete the diamond puzzle by substituting in the numbers from the problem. Example: x2 + 5x – 6  

NOTE: To find the numbers that fit on the left and right, list the factors of the number at the top of the diamond. Remember to leave them grouped together.Example: Factors of -6 are 1 x -6; 2 x -3; 3 x -2; and 6 x -1The group of factors that add together to equal the number at the bottom of the diamond is the answer.Example: 1 + -6 = -5; 2 + -3 = -1; 3 + -2 = 1; and 6 + -1 = 5

twins

Step 2: Rewrite the problem substituting the answer to the diamond puzzle (with variable attached) for the middle term: 

1x2 + 5x – 6

1x2 ________ – 6 

Step 3: Group the first two and the last two terms, then factor each group by GCF: 

(_______) + (_______)

__(_____) + __(_____)

 

- 1x + 6x

1x² - 1x 6x - 6

x x - 1 6 x - 1

The answer!

twinsTerms outside of the twins

16

7

6

Step 4: The two sections in parenthesis should always match. Then rewrite the expression as follows:

(______)(______)

Example: Factor 2x2 + 7x + 3

step 1:

step 2: step 3:  step 4: (x + 3)(2x + 1)

x(2x + 1) + 3(2x + 1)

2x2 + 1x + 6x + 3

x + 6 x - 1

More Practice! Factor the following trinomials.

1. x2 + 12x + 32

2. x2 + 22x + 121

3. 28x2 + 60x – 25

4. 48x2 + 22x – 15

(x + 4)(x + 8)

(x + 11)(x + 11) or (x + 11)2

(2x + 5)(14x - 5)

(6x + 5)(8x - 3)

NOTEBOOK TEST!

You only have 20 minutes!!