﻿ Definition of Removing a Common Factor | Define Removing a Common Factor - Geometry - Free Math Dictionary Online

# Removing a Common Factor

## 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

### Example of Removing a Common Factor

• In the expression 2x + 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 5t3 as common factor in the numerator and 5t2 in the denominator.

### Solved Example on Removing a Common Factor

#### Ques: Factor: 9x4 + 18x

##### Choices:
A. 3x (3x3 + 6x)
B. 9x (x3 + 2)
C. 9x (x3 - 2)
D. 3x2 (3x2 + 6)

#### Solution:

tep 1: 9x4 + 18x [Given expression.]
Step 2: 9x4 = 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: 9 x4 + 18x = 9x (x3 + 2) [Use the distributive property to factor the greatest common factor out of the polynomial.]

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