Monomials and Factoring

Honors Math – Grade 8

KEY CONCEPT Prime and Composite Numbers

A whole number, greater than 1, for which the only factors are 1 and itself is called a prime number.

A whole number, greater than 1, that has more than two factors is called a composite number.

Examples: 2, 3, 4, 5, 11, 13, 17, 19

Examples: 4, 6, 8, 9, 10, 12, 14, 15, 200

0 and 1 are NEITHER prime nor composite.

Find the prime factorization of 90

Make a factor tree 90What are some

factors of 90 that are not prime?

Recall: factors are numbers multiplied to obtain a product.

9 10Are 9 and 10 prime?

Write factors for each number that

is composite.3 3 5 2

Circle the prime numbers.

53290 2 A whole number expressed as the product of prime numbers is called the prime factorization of the number.

Factor the monomial completely

A monomial is in factored form when it is expressed as the product of prime numbers and variables, and no variable has an exponent greater than 1.

3212 ba

-12 = -1 x 12

32121 ba

Write the prime factorization of 12.

12 = 2 x 2 x 3

323221 ba

Write the exponents in expanded form.

bbbaa 3221

Find the GCF of 48 and 60Write the prime factorization of each number. “Factor” each number.

48

4 12

22 3 4

22

60

5 12

3 4

22

2235603222248

Circle the common prime factors.

The common prime factors are 2, 2, and 3.

The product of the common prime factors is called the greatest common factor (GCF).

The GCF of 48 and 60 = 2 x 2 x 3 = 12

KEY CONCEPT Greatest Common Factor (GCF)

The GCF of two or more monomials is the product of their common factors when each monomial is written in factored form.

If two or more integers or monomials have a GCF of 1, then the integers or monomials are said to be relatively prime.

Find the GCF &yx236 zxy254

Circle the common prime factors.

Factor each number.

yxxyx 332236 2

zyyxzxy 333254 2

The GCF is the product of common prime factors.

yxGCF 332 xy18

Find the GCF &317d 25d

Circle the common prime factors.

Factor each number.

dddd 17117 3

ddd 515 2

The GCF is the product of common prime factors.

ddGCF 1 2d

GCF33222 18,6,42 bababa

Circle the common prime factors.

Factor each number.

baaba 73242 2

bbbaaaba 33218 33

The GCF is the product of common prime factors.

baaGCF 32 ba26

bbaaba 326 22