Factoring
A polynomial is factored when it is written as a product of two or more
polynomials. Factoring a polynomial is the reverse process of expanding.
The Greatest Common Factor (GCF) is the greatest number and/or variable that is a factor
of two or more numbers or terms.
1) What is the Greatest Common Factor (GCF) for the
following examples?
a) 36 and 60
To find the Greatest Common Factor:
1. Find the GCF from the coefficients
2 2
b) 12𝑥 𝑦 and6𝑥𝑦
2. Determine which variables are common
amongst the terms the greatest number of
2 2 each variable in common is the GCF (lowest
c) 5𝑥𝑦 and 20𝑦
exponent)
4 3 2 5 3
d) 21𝑐 𝑑 and 28𝑐 𝑑 and 7𝑐𝑑
Factoring a Polynomial
1. Find the GCF of the terms
2. Write the GCF as the first factor outside a set of brackets
3. Divide each term by the GCF, writing the result inside the brackets
2) Monomial Common Factor: Factor fully, if possible.
2
a)6𝑥 + 3 b) 8𝑥 + 7𝑥
6 4 3 4 2 2 2 3
c) 25𝑘 + 15𝑘 d) 2𝑥 𝑦 𝑧 + 4𝑥 𝑦 𝑧
3 1 4 2 1 3 1 2 2
2
e) 3 𝑎 −
1
𝑎𝑏 f) 6 𝑘 𝑚 − 2
𝑘𝑚 + 3
𝑘𝑚
3
A polynomial is factored when it is written as a product of two or more
polynomials. Factoring a polynomial is the reverse process of expanding.
The Greatest Common Factor (GCF) is the greatest number and/or variable that is a factor
of two or more numbers or terms.
1) What is the Greatest Common Factor (GCF) for the
following examples?
a) 36 and 60
To find the Greatest Common Factor:
1. Find the GCF from the coefficients
2 2
b) 12𝑥 𝑦 and6𝑥𝑦
2. Determine which variables are common
amongst the terms the greatest number of
2 2 each variable in common is the GCF (lowest
c) 5𝑥𝑦 and 20𝑦
exponent)
4 3 2 5 3
d) 21𝑐 𝑑 and 28𝑐 𝑑 and 7𝑐𝑑
Factoring a Polynomial
1. Find the GCF of the terms
2. Write the GCF as the first factor outside a set of brackets
3. Divide each term by the GCF, writing the result inside the brackets
2) Monomial Common Factor: Factor fully, if possible.
2
a)6𝑥 + 3 b) 8𝑥 + 7𝑥
6 4 3 4 2 2 2 3
c) 25𝑘 + 15𝑘 d) 2𝑥 𝑦 𝑧 + 4𝑥 𝑦 𝑧
3 1 4 2 1 3 1 2 2
2
e) 3 𝑎 −
1
𝑎𝑏 f) 6 𝑘 𝑚 − 2
𝑘𝑚 + 3
𝑘𝑚
3
