1.
Multiply: 2x(5x + 3)
2.
What are the factors of 8? What does it
mean to be a factor of a number?
3.
Which of the following numbers are
prime?
3, 4, 5, 6, 7, 8, 9, 10, 11




Students will be able to determine
whether a number is prime or composite
and give its prime factorization.
Students will be able to give the prime
factorization of a monomial.
Students will be able to find the greatest
common factor of a polynomial.
Students will be able to use the
distributive property to factor out the GCF
from a polynomial.



A prime number is a number that can only
be divided by 1 and itself.
A composite number is a number that is not
prime.
Prime or composite? 15
19
23
27

I will give you a sticky note with a number on it. Decide
whether the number is prime or composite then place it
in the correct category on the board.
Prime
Composite



Prime factorization means finding all of
the prime factors of a number.
To find the prime factorization, make a
factor tree!
Example: 84

Give the prime factorization of:
1. 40
2. 210




Remember how we broke down monomials
when we wanted to multiply/divide them?
Example: 9a4b3
To give the prime factorization of a
monomial, use the same process. Just
remember to ALSO factor the coefficient.
Example: 9a4b3
Give the prime factorization:
1. 16xy2
2. 24m4n2

The Greatest Common Factor (GCF) of
two or more numbers is the largest number
that can divide into all of the numbers.


To find the GCF, start by writing out the
prime factorization. What factors do the
numbers have in common? Circle these
then multiply the common factors to get
your answer.
Example: find the GCF of 42 and 60.

Find the GCF of 36 and 60.

Find the GCF of 27 and 81.

Example: Find the GCF of 40a2b and 48ab4.
1.
Find the GCF of 12a3b4 and 3a5b.
2.
Find the GCF of 7x2y2 and 10xy3.



Pick a partner!
Move your desks together.
Take your notes and calculator with you!

Race your partner to complete the
problems. Whoever finishes all of the
problems first (they must be done
correctly) will win a prize! Let me know
when you are done so that I can check
your work!
I.
1. composite: (7)(3)
2. composite: (3)(3)(2)(2)
3. prime
4. composite: (17)(2)(2)
II. 1. (3)(2)(2)(2)(a)(a)(b)(b)(b)(b)(b)(b)
2. (5)(5)(2)(x)(x)(x)(x)(y)
III. 1. 5
2. 3r2s2
3. 13xy

Just find the GCF of all of the terms.

Example: 3x3y – 9x2y2

Example: 12x3 – 8x2 + 16x

18z3 + 9z2 – 6z

12a2b + 24a – 48b

What operation undoes addition for
numbers?

What operation undoes division for
numbers?

How can we undo multiplication for
polynomials?

Multiply: 2x(5x + 3)

We can work backwards. What if I gave
you the answer 10x2 + 6x, and asked you
for the original problem?

We did this with basic problems in August
and September.

How can we “undistribute” (10x – 5)?



Fancy math language: Find the GCF then
use the distributive property to factor out
the GCF.
What are we really doing? Take out the
GCF and then write your “leftovers” on the
inside.
Example: 10x2 + 6x

Factor out the GCF from each of the
following:
1. 3x3y – 9x2y2
2. 12x3 – 8x2 + 16x

Factor out the GCF from each of the following:

18z3 + 9z2 – 6z

12a2b + 24a – 48b
Factor out the GCF of each of the following:
24c5 – 16c2d
19x2y + 9xy2
32x3 – 4x – 16
Factor out the GCF of each of the following:
1. 9x2 – 12x + 3
2. 12x3 + 6x2 + 36
3. What does it mean to FACTOR a number,
monomial, or polynomial?
Write 2-3 sentences.
When you finish, write your name on it and
turn it into Mrs. S!
Give the prime factorization of each of the following:
1. 200
2. 34a4b3c
Find the GCF of each of the following:
3. 144, 36
4. 144x2y4, 36x5y3
Factor out the GCF:
5. 144x2y4 + 36x5y3
6. 14x2 – 7x + 21