Warm-up 3-27
1. Identify the Greatest
Common Factor (GCF):
𝑎) 24 𝑎𝑛𝑑 32 𝑏) 12𝑥 4 𝑎𝑛𝑑 15𝑥 5
Factor the trinomials
4. 𝑥 2 + 11𝑥 + 18
7. 6𝑥 2 − 𝑥 − 2
Factor each binomial
2
4
2. 25𝑥 − 16
3. 4𝑥 + 36
6. 3𝑥 2 + 15𝑥 − 150
5. 𝑥 2 − 8𝑥 + 9
8. 5𝑥 2 − 13𝑥 + 8
Factor out the GCF:
9. 5𝑥 2 𝑦 + 15𝑥𝑦 2 − 20𝑥𝑦
Unit 7 Day 8: Factoring
Polynomials With More
Than 3 Terms
Essential Question: How can we factor a
polynomial with more than three terms?
Review of Factoring using the GCF
Greatest Common Factor (GCF) – the greatest factor shared
by two or more polynomials
3
2xy
-
2
3
12x y
3
2xy (1
- 6x)
This is always the first method you use when you factor!
Factor by Grouping Method
To factor a polynomial with four terms using the grouping
method:
x3 + 3x2 + 2x + 6
1. “Group” the first two terms and the last two terms using
parentheses
(x3 + 3x2)(+ 2x + 6)
2. Factor out the GCF from both groups
x2(x + 3) + 2(x + 3)
3. Factor out the binomial GCF (what is left in the parentheses)
(x2 + 2)(x + 3)
What are some things we need to
remember?
• Before you start grouping, make sure you
factor out a GCF if it is common to all four
terms!
• If you do not have the same remainder
once you have factored the GCF out of
each group, that means that your
polynomial cannot be factored anymore!
Practice!
2x3 + x2 + 8x + 4
20n3 + 12n2 + 25n + 15
(2x3 + x2)(+ 8x + 4)
(20n3 + 12n2)(+ 25n + 15)
x2(2x + 1)+ 4(2x + 1)
4n2(5n + 3)+ 5(5n + 3)
Same thing!
(4n2 + 5)(5n + 3)
(x2 + 4)(2x + 1)
Practice!
x3 + 3x2 – 5x – 15
3
(x
+
2
3x )(–
5x – 15)
2x3 – x2 – 10x + 5
3
(2x
–
2
x )(–
10x + 5)
x2(x + 3) – 5(x + 3)
x2(2x – 1) – 5(2x – 1)
(x2 – 5)(x + 3)
(x2 – 5)(2x – 1)
Practice!
2x3 + 10x2 + 8x + 40
Factor out GCF: 2[x3 + 5x2 + 4x + 20]
Group: 2[(x3 + 5x2)(+ 4x + 20)]
Group GCF: 2[x2(x + 5) + 4(x + 5)]
Factored Form: 2(x2 + 4)(x + 5)
Summary
In the summary portion of your notes, answer your
essential question and any other questions.
Essential Question: How can we factor a
polynomial with more than three terms?