Factoring Out GCF in Polynomials

Factoring

Polynomials

Unit 14

Greatest
Common

Factor

Lesson 1

What? Why? How?

We are learning how to
find the gcf from an
expression/polynomial
and how to decompose
polynomials into
irreducible factors.

WHAT ARE WE

LEARNING

WHY ARE WE

LEARNING THIS

HOW YOU’LL BE

SUCCESSFUL

We are learning how to
factor polynomials in order
to solve for
x-intercepts/zeros. Factoring
is the foundation for many
theorems and problems that
student will later learn in
precalculus and calculus.

● I can find the gcf.
● I can use factoring to

write a polynomial as the
product of polynomials of
lesser degree.

Greatest Common Factors (GCF)

The greatest common factor of an algebraic expression is the
"greatest" factor that can be divided into each of the terms with no
remainder.

For example: 24 and 36 have a GCF of 12 because 12 goes into 24
two times and 36 three times. 24 and 36 have other factors but 12 is
the largest number to go into both.

Greatest Common Factors (GCF)

What are the factors of 36 and 24?

24-

36-

What is the largest factor they have in common?

Fill in the Blank

The greatest common factor (GCF) of 24 and 36 is

Greatest Common Factors (GCF)

1. 25a² + 15a

2. 18x² - 12x³

3. 28a²b + 56abc²

Fill in the Blank

The greatest common factor (GCF) of each term of 25a² + 15a

Math Response

The greatest common factor (GCF) of each term of 18x² - 12x³

Type answer here

Correct Answer: 6x^2

Deg^°

Rad

Math Response

The greatest common factor (GCF) of each term of 28a²b + 56abc²

Type answer here

Correct Answer: 28ab

Deg^°

Rad

Multiple Choice

What is the GCF? 5x²+20x

• 5
• x
• 5x
• 20x

Multiple Choice

What is the GCF? 3x²-2x

• 3
• 3x
• x
• 2

Multiple Choice

Factor:
x² - 5x

• 1(x - 5)
• x(x - 5x)
• x(x - 5)
• x²(1 - 5)

Multiple Choice

Factor: 3x³ + 9x² - 15x

• x(3x² + 9x - 15)

• 3x(x² + 3x - 5)

• 3x(x² - 9x + 15)

• x(3x² -9x + 15)

Greatest Common Factors (GCF)

1. 20x² - 24xy

2. 28a² + 21b - 35b²c²

Math Response

Factor completely

$$20x^2-24xy$$  

Type answer here

Correct Answer: 4x\left(5x-6y\right)

Deg^°

Rad

Math Response

Factor completely

$$28a^2+21b-35b^2c^2$$  

Type answer here

Correct Answer: 7\left(4a^2+3b-5b^2c^2\right)

Deg^°

Rad

Multiple Choice

Factor completely

$$4a^3b^5\ -\ 18a^2b^3\ +\ 8a^3b^3$$  

• $$2a^2b^3\ \left(2ab^2\ -\ 9ab\ +\ 4ab^2\right)$$  

• $$2a^2b^3\ \left(2ab^2\ -\ 9\ +\ 4a\right)$$  

• $$4a^2b^3\ \left(ab^2\ -\ 14\ +\ 6a\right)$$  

• $$2ab\ \left(2a^2b^3\ -\ 9ab\ +\ 4ab\right)$$  

Multiple Choice

Find the factors

$$24m^4n^2\ -\ 16m^3n^3$$  

• $$4m^3n^2\left(6m\ -\ 4n\right)$$  

• $$8mn\ \left(3m^4n^2\ -\ 2m^3n^3\right)$$  

• $$8m^3n^2\ \left(3m\ -\ 2n\right)$$  

• $$8m^3n^2\ \left(3mn\ -\ 2mn\right)$$  

Math Response

Factor out GCF completely:

16xy² - 24y²z + 40y²

Type answer here

Correct Answer: 8y^2\left(2x-3z+5\right)

Deg^°

Rad

Math Response

Factor Completely (upload work)

$$16xy^2-24x^2yz+40y^2$$

Type answer here

Correct Answer: 8y\left(2xy-3x^2z+5y\right)

Deg^°

Rad

Math Response

Factor out GCF completely:

16xy² - 24y²z + 40y²

Type answer here

Correct Answer: 8y^2\left(2x-3z+5\right)

Deg^°

Rad