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What is the completely factored form of 21x^3 - 9x^2 + 15x?
A3x(7x^2-3x+15)
B3x(7x^2-3x+5)
C3x(7x^2+3x+5)
D3x(7x^2-3x-5)
Answer & Solution
Correct answer: B. 3x(7x^2-3x+5)
1. The GCF of 21x cubed, 9x squared, and 15x is 3x, found by matching common prime and variable factors.
2. Rewrite each term using the GCF: 21x cubed is 3x times 7x squared, 9x squared is 3x times 3x, and 15x is 3x times 5.
3. Factor to get 3x(7x squared minus 3x plus 5).
4. Check by multiplying: 3x times 7x squared, minus 3x times 3x, plus 3x times 5, gives back 21x cubed minus 9x squared plus 15x.
5. Using the GCF 3 instead of 3x leaves an x factor stranded outside the parentheses in every term, which is not a fully factored answer.
_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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