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

      Example of Remainder
  • 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.

Video Examples: Removing a Common Factor


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)
    Correct Answer: B

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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