** Definition of Removing a Common Factor**

- Removing a Common Factor means taking away a factor, generally the greatest common factor between two or more polynomials.

**More about Removing a Common Factor**

- We generally need to remove a common factor or the greatest common factor in factorization or while simplifying an algebraic expression.
- The greatest common factor is always unique between two or more polynomials.

**Examples of Removing a Common Factor**

- In the expression 2
*x*+ 18, the common factor is 2, so 2 can be removed and the expression can be rewritten in factor form as 2(*x*+ 9) - To simplify the expression , we can take 5
*t*^{3}as common factor in the numerator and 5*t*^{2}in the denominator. So,

**Solved Example on Removing a Common Factor**

Factor:

9x^{4}+ 18x

Choices:

A.3x(3x^{3}+ 6x)

B.9x(x^{3}+ 2)

C.9x(x^{3}- 2)

D.3x^{2}(3x^{2}+ 6)

Correct Answer: B

Solution:

Step 1:9x^{4}+ 18x[Given expression.]

Step 2:9x^{4}= 3 · 3 ·x·x·x·x[Factor.]

Step 3:18x= 3 · 3 · 2 ·x

Step 4:The GCF = 3 · 3 ·x= 9x[It is the product of all the common factors.]

Step 5:9x^{4}+ 18x= 9x(x^{3}+ 2) [Use the distributive property to factor the greatest common factor out of the polynomial.]

**Related Terms for Removing a Common Factor**

- Binomial
- Common Factor
- Divide
- Exponent
- Expression
- Factor
- Greatest Common Factor (GCF)
- Integer
- Monomial
- Number
- Polynomial
- Term
- Variable