Finding Common Factors
This worksheet focuses on identifying and applying common factors to algebraic expressions for Grade 11 students.
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Finding Common Factors
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Read each question carefully and follow the instructions to find the common factors of the given expressions.
1. What is the greatest common factor (GCF) of the terms in the expression 12x^3y^2 - 18x^2y^4?
6x^2y^2
3x^2y^2
6xy
12x^3y^4
2. Which of the following is a common factor of 20a^2b and 35ab^3?
5a^2b^3
5ab
7ab
ab
3. The greatest common factor of 15m^4n^2 and 25m^2n^5 is .
4. When factoring out the GCF from 6x^2y + 9xy^2, the remaining expression is .
5. Find the greatest common factor of the terms in the polynomial 4x^3 - 8x^2 + 12x.
6. Factor the expression 7a^2b^3 - 14ab^2 + 21a^3b completely by factoring out the GCF.
7. The GCF of 30p^5q^2 and 45p^3q^4 is 15p^3q^2.
True
False
8. The expression 5x(y + 3) has a common factor of (y + 3).
True
False
Match the expression with its greatest common factor.
9. 10x^2 + 15x
a. 4y
10. 8y^3 - 12y^2
b. 5x
11. 14mn + 7m
c. 4y^2
12. 16a^4b - 20a^2b^3
d. 7m
e. 4a^2b
13. Consider the expression 3x^2(x - 2) + 5(x - 2). What is the common binomial factor?
14. Factor the expression (a + b)x - (a + b)y completely.