Transcript x + 4

Find the GCF of each pair of monomials:
1.
3x2, 9x3
3x²
2
3
3
2
2.
p q ,p q
3.
27ab2, 48bc p²q²
3b
Factor:
4.
10b + 25b4 5b(2 + 5b³)
5.
-35x3y5 + 7x2y 7x²y(-5xy4 + 1)
6.
4a + 8b + 12
4(a + 2b + 3)
Solve.
7.
19x = 76
x=4
8.
-2x + 18 = -72 – 5x
x = -30
9.
x–4=5
3
x = 27
Diamond Puzzle
Please complete the following puzzles.
-18
-24
3
6
-8
12
-5
2
8
-3
3
6
-44
11
-4
7
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.
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
a•c
1 •(-6)
-6
-1
6
b
5
5
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 -1
The 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
Step 2: Rewrite the problem substituting the answer to the
diamond puzzle (with variable attached) for the middle term:
1x2 + 5x – 6
- 1x + 6x – 6
1x2 ________
Step 3: Group the first two and the last two terms, then factor
each group by GCF:
1x² - 1x
6x - 6
(_______)
+ (_______)
6 x-1
x x-1
__(_____)
+ __(_____)
twins
Step 4: The two sections in parenthesis should always
match. Then rewrite the expression as follows:
(______)(______)
x+6
x-1
Terms outside of the twins
twins
Example: Factor 2x2 + 7x + 3
6
The answer!
step 1:
1
6
step 2:
2x2 + 1x + 6x + 3
step 3:
x(2x + 1) + 3(2x + 1)
step 4:
(x + 3)(2x + 1)
7
More Practice! Factor the following trinomials.
1. x2 + 12x + 32
(x + 4)(x + 8)
2. x2 + 22x + 121
(x + 11)(x + 11) or (x + 11)2
3. 28x2 + 60x – 25
(2x + 5)(14x - 5)
4. 48x2 + 22x – 15
(6x + 5)(8x - 3)
NOTEBOOK TEST!
You only have 20 minutes!!