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
9x4 + 18x
A.3x(3x3 + 6x)
B.9x(x3 + 2)
C.9x(x3 - 2)
D.3x2(3x2 + 6)
Correct Answer: B
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
- Common Factor
- Greatest Common Factor (GCF)