Name______________________________
Date________
Unit: Factoring
Period_______
Introduction to Factoring
Do Now: Write the prime factorization of 60.
Factors shared by two of more whole numbers are called common factors. The greatest of these
common factors is called the _______________ ______________ _______________.
Part I: Factors and Greatest Common Factors
1. Find the GCF of each set of numbers
a. 24 and 60
b. 18 and 27
c. 12 and 16
d. 16, 24, 48
You can find the GCF of monomials that include variables. To find the GCF of monomials, write the prime
factorization of each coefficient and write all the powers of variables as products. Then find the product
of the common factors.
2. Find the GCF of each set of monomials
a. 3x3 and 6x2
b. 18g2 and 27g3
c. 4x2 and 5y3
d. 8a4b3, 4a3b3, 12a2b3
Part II: Factoring by using the GCF
A polynomial is in its factored form when it is written as a product of monomials and polynomials that
cannot be factored further.
3. Factor each polynomial. Check your answer.
a. 4x2 – 3x
b. 10y3 + 20y2 – 5y
c. -12x – 8x2
d. 8x4 + 4x3 – 2x2
e. Mariah’s calculator is powered by solar energy. The area of the solar panel is (7x 2 + x) cm2.
Factor this polynomial to find possible expressions for the dimensions of the solar panel.
Part III: Summary
1. How do you find a common factor?
2. Explain how finding the GCF of monomials helps you to factor a polynomial.
3. How can you check your answer?
4. Can the polynomial 2x3 – 7x3 be factored further?
Part IV: Extra for Experts!
Directions: Factor each polynomial. Check your answer.
a. 9y2 + 45y
b. 21c2 + 14c
c. -5g3 – 15g2
d. A model rocket is fired vertically in the air at 320 ft/s. The expression -16t2 + 320t gives the
rocket’s height after t seconds. Factor this expression.
Name__________________________________
Date______
Unit: Factoring Polynomials
Period_____
Factoring Quadratic Trinomials
Do Now: Use the FOIL method to find the product of (x + 2) and (x + 3).
Think about it:

Where did the x2 come from?

Where did the 5x come from?

Where did the 6 come from?
Part I: Factoring in the form x2 + bx + c
To factor a quadratic trinomial of the form x2 + bx +c, find two factors of c whose sum is b.
a. Factor x2 + 9x + 18

Start with a ‘Double Bubble’!

List the factors of 18

Find the pair of factors whose sum is 9.

Write these factors inside the bubble.

Use the FOIL method to check
b. Factor x2 -10x + 16
c. Factor x2 -8x - 20
d. Factor x2 + 7x - 18
Answer:__________________
Part II: Looking at the Signs - Graphic Organizer
Look at the signs of the factors in the above examples. Fill in the table below. Look to see what
conclusions you can come up with.
b
+
–
–
+
c
+
+
–
–
Example
x2 + 9x + 18
x2 -10x + 16
x2 -8x - 20
x2 + 7x - 18
Factors
Part III: Examples
Directions: Factor each trinomial. Check your answer.
x2 + 6x + 8
x2 + 5x + 6
x2 + 5x + 4
x2 – 6x + 8
x2 – x – 6
x2 + 3x – 18
y2 + 10y + 21
x2 + 13x + 42
g2 – 2g – 3
p2 – 11p + 18
Sign of Factors
Name__________________________________
Date______
Unit: Factoring Polynomials
Period_____
Difference of Two Squares (DOTS)
SWUT: Special products can be factored easily by using patterns.
A polynomial is a difference of two squares if:

There are two terms, one subtracted from the other.

Both terms are perfect squares.
Difference of Two Squares
a2 – b2 = (a + b) (a – b)
x2
Example
– 9 = (x + 3) (x – 3)
Directions: Determine whether the binomial is a difference of two squares. If so, factor. If not, explain.
1. x2 – 81
2. 9p4 – 16q2
3. x6 – 7y2
4. 1 – 4x2
5. 16x2 – 4y5
Summary:
1. Explain why the product of the binomials in the form (a + b)(a – b) is NOT a trinomial?
2. Name the characteristics of a difference of squares polynomial.
Name__________________________________
Date______
Unit: Factoring Polynomials
Period_____
Factoring Completely
SWUT: To factor a polynomial completely, we may need to use more than one factoring method.
Recall that a polynomial is in its fully factored form when it is written as a product that cannot be
factored further.
Part I: Determining whether a Polynomial is Completely Factored
Directions: Tell whether each polynomial is completely factored. If not, factor it.
a. 2x(x2 + 4)
b. (2x + 6)(x + 5)
c. 5x2(x – 1)
Part II: Factoring Completely
Directions: Factor each polynomial completely.
d. 3x2 – 15x3 + 12x2
e. 3x5 – 12x3
f. 2x4 + 18
g. 2p5 + 10p4 – 12p3
h. 24r2 – 6r4
i.
4x3y – 4x2y – 8xy
j.
5x2 – 10x + 14