REMOVING A COMMON FACTOR

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.]

Quick Summary

Identify the greatest common factor (GCF) of all terms.
Divide each term by the GCF.
Write the GCF outside parentheses, followed by the remaining terms inside the parentheses.

\[ a(b+c) = ab + ac \]

🍎 Teacher Insights

Emphasize the distributive property as the reverse operation of removing a common factor. Use visual aids to illustrate the factorization process. Provide ample practice problems with varying levels of difficulty.

🎓 Prerequisites

Factoring
Greatest Common Factor (GCF)
Distributive Property
Polynomials

Check Your Knowledge

Q1: Factor the expression: 4x + 12

A. 4(x + 12) B. 2(2x + 6) C. 4(x + 3) D. x(4 + 12)

Q2: Factor the expression: 6y^2 - 9y

A. 3y(2y - 3) B. 3(2y^2 - 3y) C. y(6y - 9) D. 6y(y - 9)

Frequently Asked Questions

Q: What is the point of removing a common factor?
A: It simplifies expressions, makes them easier to work with, and is a key step in solving equations and further factorization.

Q: How do I find the greatest common factor?
A: List the factors of each term and identify the largest factor they have in common, considering both coefficients and variables.