This document discusses common monomial factoring, which is writing a polynomial as a product of two polynomials where one is a monomial that factors each term. It provides examples of finding the greatest common factor (GCF) of terms in a polynomial and using it to factor the polynomial. Specifically, it factors polynomials like 4m^2 + 10m^4, 6x^4 + 9x^2y + 15x^5y, and 25b^3c^2 - 5b^2c.

1. Polynomial with
Common
Monomial Factor
Lesson 1

2. Common monomial factoring is the process of
writing a polynomial as a product of two polynomials,
one of which is a monomial that factors each term of
the polynomial.
To ensure that the polynomial is the prime
polynomial, use the Greatest Common Factor (GCF) of
the terms of the given polynomials.

3. 1. Find the GCF of 4𝒎 𝟐
and 𝟏𝟎𝒎 𝟒
.
𝟒𝒎 𝟐
𝟏𝟎𝒎 𝟒
𝑮𝑪𝑭
𝑮𝑪𝑭 2 𝒎 𝟐

4. 2. Find the GCF of 𝟔𝒙 𝟒 , 9𝒙 𝟐y, and 𝟏𝟓𝒙 𝟓 𝒚.
Solution:
Express each as a product of prime factors.
𝟔𝒙 𝟒
9𝒙 𝟐y
𝟏𝟓𝒙 𝟓 𝒚
= 𝟐 ∗ 3 ∗ x ∗ x ∗ x ∗ x
= 𝟑 ∗ 3 ∗ x ∗ x ∗ y
= 5 ∗ 3 ∗ x ∗ x ∗ x ∗ x ∗ x ∗
𝑮𝑪𝑭 = 𝟑 ∗ x ∗ x
𝑮𝑪𝑭 = 3𝒙 𝟐
y

6. Factor 𝟏𝟎𝒚 𝟒
+ 5𝒚 𝟑
.
10 𝒚 𝟒
5𝒚 𝟑
𝑮𝑪𝑭
𝑮𝑪𝑭 5 𝒚 𝟑

7. 𝟏𝟎𝒚 𝟒 + 5𝒚 𝟑 = 5 𝒚 𝟑
(
𝟏𝟎𝒚 𝟒
5 𝒚 𝟑
2
=10 ÷ 5 2
𝒚 𝟒
𝒚 𝟑
= 𝒚 𝟒−𝟑
=
= y
y
=
+
5 𝒚 𝟑
5 𝒚 𝟑
= 1
1 )

9. Factor 𝟐𝟓𝒃 𝟑
𝒄 𝟐
− 5𝒃 𝟐
𝒄
Step 1: Find the Common Factor
𝟐𝟓𝒃 𝟑 𝒄 𝟐 = 𝟓 ∗ 𝟓 ∗ b ∗ b ∗ b ∗ c ∗ c
𝟓𝒃 𝟐 𝒄 = 𝟓 ∗ b ∗ b ∗ c
GCF = 𝟓 ∗ b ∗ b * c
GCF =

10. Step 2: Divide out the Common Factor.
𝟐𝟓𝒃 𝟑
𝒄 𝟐
− 5𝒃 𝟐
𝒄 = 5𝒃 𝟐 𝒄 (
𝟐𝟓𝒃 𝟑
𝒄 𝟐
𝟓𝒃 𝟐
𝒄
= 𝟐𝟓 ÷ 𝟓 = 5
5
𝒃 𝟑 𝒄 𝟐
𝒃 𝟐 𝒄
= 𝒃 𝟑−𝟐 𝒄 𝟐−𝟏 = bc
bc -
5𝒃 𝟐
𝒄
5𝒃 𝟐 𝒄
= 1
1 )