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Factoring Polynomials: GCF

Question 5 • Common Core Algebra I B-IC

Which statements are true about the polynomial 28vw + 49v + 35w? Check all that apply.

Answer
A
The coefficients have no common factors other than 1.
B
There are no common variables among all three terms.
C
The GCF of the polynomial is 7v.
D
Each term written as the product, where one factor is the GCF, is 7(28vw) + 7(49v) + 35(w).
E
The resulting expression when factoring out the GCF is 7(4vw + 7v + 5w).

Explanation

The greatest common factor of the coefficients 28, 49, and 35 is 7. No variable appears in all three terms, so the polynomial’s GCF is 7, not 7v. Factoring out 7 gives 7(4vw + 7v + 5w), so the true statements are that there are no common variables among all three terms and that the factored expression is 7(4vw + 7v + 5w).

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