NAME Teacher’s Notes
Date _____________ Period _________
8.1 – 8.2 Factors and Greatest Common Factors
Algebra 1 ACC
Objectives:

Write the prime factorization of numbers.

Find the GCF of monomials.

Factor polynomials by using the greatest common factor.
Prime factorization:
Example 1: Write the prime factorization of 98.
Example 2: Write the prime factorization of each number.
a. 40
b. 33
Your Turn!
c. 48
Greatest Common Factor (GCF):
Example 3: Find the GCF of each pair of numbers. 100 and 60.
GCF (100, 60) = 20
Example 4: Find the GCF of each pair of numbers. 26 and 52.
GCF (26, 52) = 26
d. 50
Your Turn: Find the GCF of each pair of numbers. 12 and 16.
Example 5: Find the GCF of each pair of monomials. 15x3 and 9x2.
GCF (15x3, 9x2) = 3x2
Example 6: Find the GCF of each pair of monomials. 9y2 and 27y3.
GCF (9y2, 27y3) = 9y2
Your Turn: Find the GCF of each pair of monomials. 18g2 and 27g3
Example 7: Find the GCF of each pair of monomials. 36xy2 and 18x2y
Example 8: A cafeteria has 18 chocolate-milk cartons and 24 regular-milk cartons. The cook wants to arrange the cartons
with the same number of cartons in each row. Chocolate and regular milk will not be in the same row. How many rows will
there be if the cook puts the greatest possible number of cartons in each row?
GCF = 6
Rows of choc milk = 18 / 6 = 3
Rows of reg milk = 24 / 6 = 4
Total rows of milk = 3 + 4 = 7
To factor a polynomial,
1. Find the GCF of the polynomial
2. Write the GCF (
3. Write the remaining factors )
4. Check your answer by distributing or multiplying in parenthesis. You should get the original polynomial.
Example 9: Factor each polynomial. Check your answer. 2x2 – 4
2 x2  4
2 x 2 4
2 2
2  x2  2
Example 10: Factor each polynomial. Check your answer. 8x3 – 4x2 – 16x
8 x 3  4 x 2  16 x
8 x 3 4 x 2 16 x
4x 4x 4x
4 x  2 x2  x  4
Example 11: Factor each polynomial. Check your answer. –14x – 12x2
14 x  12 x 2
14 x 12 x 2
2 x 2 x
2 x  7  6 x 
Example 12: Factor each polynomial. Check your answer. 3x3 + 12x2 – 9x
3 x 3  12 x 2  9 x
3 x 3 12 x 2 9 x
3x 3x 3x
3 x  x 2  4 x  3
Your Turn: Factor each polynomial. Check your answer. –14y3 – 28y2
Your Turn: Factor each polynomial. Check your answer. 25x² + 15x – 20x³
To write expressions for the length and width of a rectangle with area expressed by a polynomial, you
need to write the polynomial as a product. You can write a polynomial as a product by factoring it.
Example 13: The area of a court for the game squash is 9x2 + 6x m2. Factor this polynomial to find possible expressions for
the dimensions of the squash court.
9x2  6x
9 x 2 6 x
3x 3x
3x  3x  2 
Measurements are 3x by 3x + 2
Your Turn: The area of the solar panel on another calculator is (2x2 + 4x) cm2. Factor this polynomial to find possible
expressions for the dimensions of the solar panel.