Download Unit 7 Day 4: Factors and Factoring GCF

Warm Up 3 -3
Multiply theWarm
1. 2(𝑥 3 − 3𝑥 2 + 11)
3. 3𝑥(−12𝑥 2 + 6𝑦 3 )
Up 3 - 2 polynomials
2. 𝑥(5𝑥 2 − 10𝑥 + 2)
4. 2𝑥𝑦(−10𝑥𝑦 + 4𝑥)
Unit 7 Day 4: Factors and
Factoring GCF
Essential Questions: What is a greatest common factor? How
can we start the factoring process using the GCF?
What is factoring?

Factoring is a method to find the basic
numbers and variables that make up a
product.

(Factor) x (Factor) = Product

Some numbers are prime, meaning they
are only divisible by themselves and 1.
These can’t be factored.
What is the Greatest Common Factor?

Greatest Common Factor (GCF) –
the greatest factor shared by two or
more polynomials

ALWAYS try this factoring method
first before any other method

Divide out the biggest common
number/amount of a variable from
each of the terms
Greatest Common Factors
Find the GCF for each set of the following numbers.
Hint: list the factors and find the greatest match.
a)
b)
c)
d)
e)
2, 6
-25, -40
6, 18
16, 32
3, 8
2
-5
6
16
1
No common factors?
GCF = 1
Greatest Common Factors
Find the GCF for each set of following numbers.
Hint: list the factors and find the greatest match.
a)
b)
c)
d)
e)
f)
x, x2
x 2, x 3
xy, x2y
2x3, 8x2
3x3, 6x2
4x2, 5y3
x
x2
xy
2x2
3x2
1
No common factors?
GCF = 1
Greatest Common Factors
Factor out the GCF for each polynomial:
Factor out means you divide the GCF out (opposite of distributing).
2x + 4y
5a – 5b
18x – 6y
2m + 6mn
5x2y – 10xy
2(x + 2y)
5(a – b)
6(3x – y)
2m(1 + 3n)
5xy(x - 2)
How can you check?
FACTORING
5xy (3y – 2x2 + 5y2)
Distribute to check!
8
FACTORING
2x(x3 – 4x2 + 2x – 3)
Distribute to check!
Practice!
– 5x

2
15x

GCF = 5x

5x(3x - 1)
Practice!
–x

2
8x

GCF = x

x(8x - 1)
Practice!
2
4
8x y +
3
5
2x y

GCF =
2
3
2x y

2
3
2x y (4y

+
-
2
xy
4
3
12x y
–
2
6x )
Summary
Essential Questions: What is a greatest common factor? How
can we start the factoring process using the GCF?
Write a summary answering the
essential questions (and all of
the questions in the left side of
your notes!)