Finding Common Factors (Grade 12)
A Grade 12 math worksheet on finding common factors of algebraic expressions, including polynomials and numerical terms.
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Finding Common Factors
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Read each question carefully and determine the greatest common factor (GCF) for the given expressions or polynomials. Show all your work for full credit.
1. Find the greatest common factor (GCF) of the following monomials:
a) 12x³y² and 18x²y⁵
b) 24a⁴b³c and 36a²b⁶
Factor out the greatest common factor from each polynomial. Fill in the blank with the factored expression.
2. 5x² + 10x =
3. 9y³ - 18y² + 27y =
4. 4a⁴b² - 8a³b³ + 12a²b⁴ =
5. What is the greatest common factor of 14m²n³ and 21m⁴n?
7m²n
7m⁴n³
3m²n
42m⁴n³
Determine if the following statements are true or false.
6. The GCF of 6x²y and 15xy³ is 3xy.
True
False
7. The GCF of (x+2)(x-1) and (x+2)(x+3) is (x+2).
True
False
8. A rectangular garden has an area represented by the polynomial 10x²y - 15xy² + 5xy. If the width of the garden is the greatest common factor of its terms, what are the expressions for the width and the length of the garden?
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