Fabulous Factoring
Yesterday we factored quadratics using the diamond method. We will build on that skill today with a
FABULOUS new twist. Today you will learn to factor expressions COMPLETELY!
In front of each set of parentheses is the Greatest Common Factor (GCF) of the polynomial. Fill in the
appropriate expression inside the parentheses. How do you know the expressions are equivalent? Show why.
1. 2𝑥 2 + 12 = 2(
?
)
2. −𝑥 2 + 15𝑥 = −𝑥(
3. 3𝑥 2 − 18𝑥 = 3𝑥(
)
?
?
)
Teacher Checkpoint: Call the teacher over
First factor out the GCF like you did from problems 1-3. Then use the diamond method or the generic
rectangle to factor the expression inside the parentheses. Remember to include the GCF in your final
factorization. Problem 4 has been done for you.
4. 2𝑥 2 + 12𝑥 + 16 = 2(𝑥 2 + 6𝑥 + 8)
2(𝑥 + 4)(𝑥 + 2)
↑
Completely Factored
5. 5𝑥 2 + 5𝑥 − 10 =
6. 8𝑥 2 − 28𝑥 − 60 =
7. 3𝑥 2 − 12𝑥 − 15 =
8. −4𝑥 2 + 14𝑥 − 6 =