5 Minute Check
Simplify each expression. Complete in your
notes.
1. (-3x - 2) - (7x + 9)
2. (-2x - 1) - (x - 7)
3. (9x + 5) - (6x - 8)
4. (-8x + 1) - (8x - 1)
5 Minute Check
Simplify each expression. Complete in your
notes.
1. (-3x - 2) - (7x + 9)
5 Minute Check
Simplify each expression. Complete in your
notes.
1. (-3x - 2) - (7x + 9)
-3x - 2 - 7x - 9
-10x - 11
5 Minute Check
Simplify each expression. Complete in your
notes.
2. (-2x - 1) - (x - 7)
5 Minute Check
Simplify each expression. Complete in your
notes.
2. (-2x - 1) - (x - 7)
-2x - 1 - x + 7
-3x + 6
5 Minute Check
Simplify each expression. Complete in your
notes.
3. (9x + 5) - (6x - 8)
5 Minute Check
Simplify each expression. Complete in your
notes.
3. (9x + 5) - (6x - 8)
9x + 5 - 6x + 8
3x + 13
5 Minute Check
Simplify each expression. Complete in your
notes.
4. (-8x + 1) - (8x - 1)
5 Minute Check
Simplify each expression. Complete in your
notes.
4. (-8x + 1) - (8x - 1)
-8x + 1 - 8x + 1
-16x + 2
Monday, May 18
Lesson 7.5.8
Factor Linear Expressions
Factor Linear Expressions
Objective: To use properties of mathematics
to factor linear expressions.
Factor Linear Expressions
A monomial is a number, a variable, or a
product of a number and one or more
variables.
Monomials; 25, x, 25x
Not Monomials: x + 25, 25x + 100
Factor Linear Expressions
To factor a number means to write it as a
product of its prime factors.
36; 2 · 2 · 3 · 3
Factor Linear Expressions
A linear algebraic expression can be factored
using the same method you would use to
factor a number.
Factor Linear Expressions
Factor the expression.
12 + 30x
How to Factor Monomials. (Method 1)
Step 1 – Write both monomials as prime
factors.
Factor Linear Expressions
Factor the expression.
12 + 30x
12: 2 · 2 · 3
30: 2 · 3 · 5 · x
How to Factor Monomials.
Step 1 – Write both monomials as prime
factors.
Factor Linear Expressions
Factor the expression.
12 + 30x
12: 2 · 2 · 3
30: 2 · 3 · 5 · x
How to Factor Monomials.
Step 2 – Circle the common factors.
Factor Linear Expressions
Factor the expression.
12 + 30x
12: 2 · 2 · 3
30: 2 · 3 · 5 · x
How to Factor Monomials.
Step 2 – Circle the common factors.
Factor Linear Expressions
Factor the expression.
12 + 30x
12: 2 · 2 · 3
30: 2 · 3 · 5 · x
How to Factor Monomials.
Step 3 – Find the GCF by multiplying the
common factors for one number.
Factor Linear Expressions
Factor the expression.
12 + 30x
12: 2 · 2 · 3
30: 2 · 3 · 5 · x
GCF = 2 · 3 = 6
How to Factor Monomials.
Step 3 – Find the GCF by multiplying the
common factors for one number.
Factor Linear Expressions
Factor the expression.
12 + 30x
12: 2 · 2 · 3
30: 2 · 3 · 5 · x
GCF = 2 · 3 = 6
How to Factor Monomials.
Step 4 – Rewrite the expression with the
GCF outside the parenthesis.
Factor Linear Expressions
Factor the expression.
12 + 30x
12: 2 · 2 · 3
30: 2 · 3 · 5 · x
GCF = 2 · 3 = 6
6(2 + 5x)
How to Factor Monomials.
Step 4 – Rewrite the expression with the
GCF outside the parenthesis.
Factor Linear Expressions
Factor the expression.
8 + 12x
Step 1 – ?
Factor Linear Expressions
Factor the expression.
8 + 12x
8=2·2·2
12x = 2 · 2 · 3 · x
Step 2 – ?
Factor Linear Expressions
Factor the expression.
8 + 12x
8=2·2·2
12x = 2 · 2 · 3 · x
Step 3 –
Factor Linear Expressions
Factor the expression.
8 + 12x
8=2·2·2
12x = 2 · 2 · 3 · x
The GCF is 2 · 2 , or 4
Step 4 –
Factor Linear Expressions
Factor the expression.
8 + 12x
8=2·2·2
12x = 2 · 2 · 3 · x
The GCF is 2 · 2 , or 4
4(2 + 3x)
Factor Linear Expressions
Factor the expression.
18a + 20ab
How to Factor Monomials. (Method 2)
Step 1 – Factor out any common variables.
Factor Linear Expressions
Factor the expression.
18a + 20ab
a(18 + 20b)
How to Factor Monomials. (Method 2)
Step 1 – Factor out any common variables.
Factor Linear Expressions
Factor the expression.
18a + 20ab
a(18 + 20b)
How to Factor Monomials. (Method 2)
Step 2 – Factor out 2, if possible, and keep
factoring until you can’t.
Factor Linear Expressions
Factor the expression.
18a + 20ab
a(18 + 20b)
2a(9 + 10b)
How to Factor Monomials. (Method 2)
Step 2 – Factor out 2, if possible, and keep
factoring until you can’t.
Factor Linear Expressions
Factor the expression.
18a + 20ab
a(18 + 20b)
2a(9 + 10b)
How to Factor Monomials. (Method 2)
Step 3 – Factor out 3, if possible, and keep
factoring until you can’t.
Factor Linear Expressions
Factor the expression.
18a + 20ab
a(18 + 20b)
2a(9 + 10b)
How to Factor Monomials. (Method 2)
Step 3 – Factor out 3, if possible, and keep
factoring until you can’t.
Factor Linear Expressions
Factor the expression.
18a + 20ab
a(18 + 20b)
2a(9 + 10b)
How to Factor Monomials. (Method 2)
Step 4 – Factor out any remaining prime
numbers, if possible.
Factor Linear Expressions
Factor the expression.
18a + 20ab
a(18 + 20b)
2a(9 + 10b)
How to Factor Monomials. (Method 2)
Step 4 – Factor out any remaining prime
numbers, if possible.
Factor Linear Expressions
Factor the expression.
12 + 28c
Step 1 - ? (Method 2)
Factor Linear Expressions
Factor the expression.
12 + 28c
Step 2 - ? (Method 2)
Factor Linear Expressions
Factor the expression.
12 + 28c
2(6 + 14c)
4(3 + 7c)
Step 3 - ? (Method 2)
Factor Linear Expressions
Factor the expression.
12 + 28c
2(6 + 14c)
4(3 + 7c)
Step 4 - ? (Method 2)
Factor Linear Expressions
Factor the expression.
12 + 28c
2(6 + 14c)
4(3 + 7c)
Factor Linear Expressions
Factor the expression.
25x + 15xy
Do this on your own.
Factor Linear Expressions
Factor the expression. Method 1
25x + 15xy
25x = 5 · 5 · x
15xy = 3 · 5 · x · y
The GCF is 5 · x, or 5x
5x (5 + 3y)
Factor Linear Expressions
Factor the expression. Method 2
25x + 15xy
x(25 + 15y)
5x (5 + 3y)
Factor Linear Expressions
Factor the expression.
42mn + 14n
Do this on your own.
Factor Linear Expressions
Factor the expression. Method 1
42mn + 14n
42mn = 2 · 3 · 7 · m · n
14n = 2 · 7 · n
The GCF is 2 · 7 · n, or 14n
14n(3m + 1)
Factor Linear Expressions
Factor the expression. Method 2
42mn + 14n
n(42m + 14)
2n(21m + 7)
14n(3m + 1)
Factor Linear Expressions
Factor the expression.
3x + 9
Factor Linear Expressions
Factor the expression. Method 1
3x + 9
3x = 3 · x
9=3·3
The GCF is 3
3(x + 3)
Factor Linear Expressions
Factor the expression. Method 2
3x + 9
3(x + 3)
Factor Linear Expressions
Factor the expression.
12x + 7y
Factor Linear Expressions
Factor the expression.
12x + 7y
12x = 2 · 2 · 3 · x
7y = 7 · y
The are no common factors, the expression
cannot be factored.
Factor Linear Expressions
Factor the expression.
4x - 28
Factor Linear Expressions
Factor the expression. Method 1
4x - 28
4x = 2 · 2 · x
28 = 2 · 2 · 7
The GCF is 4
4(x - 7)
Factor Linear Expressions
Factor the expression. Method 2
4x - 28
2(2x – 14)
4(x - 7)
Factor Linear Expressions
Factor the expression.
3x + 33y
Factor Linear Expressions
Factor the expression. Method 1
3x + 33y
3x = 3 · x
33y = 3 · 11 · y
The GCF is 3
3(x + 11y)
Factor Linear Expressions
Factor the expression. Method 2
3x + 33y
3(x + 11y)
Factor Linear Expressions
Factor the expression.
4x + 35
Factor Linear Expressions
Factor the expression.
4x + 35
4x = 2 · 2 · x
35 = 5 · 7
There is no GCF and cannot be factored.
Factor Linear Expressions
Factor the expression.
32x + 18
Factor Linear Expressions
Factor the expression. Method 1
32x + 18
32x = 2 · 2 · 2 · 2 · 2 · x
18 = 2 · 3 · 3
The GCF is 2
2(16x + 9)
Factor Linear Expressions
Factor the expression. Method 2
32x + 18
2(16x + 9)
Factor Linear Expressions
Factor the expression.
27s – 54st
Factor Linear Expressions
Factor the expression. Method 1
27s – 54st
27s = 3 · 3 · 3 · s
54st = 2 · 3 · 3 · 3 · s · t
The GCF is 27s
27s(1 – 2t)
Factor Linear Expressions
Factor the expression. Method 2
27s – 54st
s(27 – 54t)
3s(9 – 18t)
9s(3 – 6t)
27s(1 – 2t)
Factor Linear Expressions
Factor the expression.
18cd + 30d
Factor Linear Expressions
Factor the expression. Method 1
18cd + 30d
18cd = 2 · 3 · 3 · c · d
30d = 2 · 3 · 5 · d
The GCF is 6d
6d(3c + 5)
Factor Linear Expressions
Factor the expression. Method 2
18cd + 30d
d(18c + 30)
2d(9c + 15)
6d(3c + 5)
Factor Linear Expressions
Factor the expression.
36x + 24
Factor Linear Expressions
Factor the expression. Method 1
36x + 24
36x = 2 · 2 · 3 · 3 · x
24 = 2 · 2 · 2 · 3
The GCF is 12
12(3x + 2)
Factor Linear Expressions
Factor the expression. Method 2
36x + 24
2(18x + 12)
4(9x + 6)
12(3x + 2)
Factor Linear Expressions
Factor the expression.
4x + 9
Factor Linear Expressions
Factor the expression.
4x + 9
x=2·2 ·x
9= 3·3
There is no GCF and cannot be factored.
Factor Linear Expressions
Factor the expression.
14x – 16y
Factor Linear Expressions
Factor the expression. Method 1
14x – 16y
14x = 2 · 7 · x
16y = 2 · 2 · 2 · 2 · y
The GCF is 2.
2(7x – 8y)
Factor Linear Expressions
Factor the expression. Method 2
14x – 16y
2(7x – 8y)
Factor Linear Expressions
Agenda Notes
Homework –
Homework Practice 7.5.8
due by the end of the period.
Circle all answers and show all work
with either method.
Chapter 7.5 Test -Wednesday, May 20