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What is the greatest common factor of 21x^3, 9x^2, and 15x?
AGCF = 3x
BGCF = 3x^2
CGCF = 9x
DGCF = x
Answer & Solution
Correct answer: A. GCF = 3x
1. Factor each coefficient into primes: 21 = 3 times 7, 9 = 3 times 3, and 15 = 3 times 5.
2. Write the variable parts in expanded form: x cubed, x squared, and x.
3. The only coefficient factor shared by all three is a single 3, and the only variable factor shared by all three is a single x, since the third term has just one x.
4. Multiply the shared factors: 3 times x gives 3x.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.1 Greatest Common Factor and Factor by Grouping_
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