Removing a Common Factor
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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 5t^{3} as common factor in the numerator and 5t^{2} in the denominator.
Video Examples: Removing a Common Factor
Solved Example on Removing a Common Factor
Ques: 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:

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