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.

Examples 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. So,

Solved Example on Removing a Common Factor

Factor:
9x4 + 18x
Choices:
A.3x(3x3 + 6x)
B.9x(x3 + 2)
C.9x(x3 - 2)
D.3x2(3x2 + 6)
Correct Answer: B
Solution:
Step 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: 9x4 + 18x = 9x(x3 + 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