Question

which statements are true about the polynomial $28vw + 49v + 35w$? check all that apply.
the coefficients have no common factors other than 1.
there are no common variables among all three terms.
the gcf of the polynomial is $7v$.
each term written as the product, where one factor is the gcf, is $7(28vw) + 7(49v) + 35(w)$.
the resulting expression when factoring out the gcf is $7(4vw + 7v + 5w)$.

Explanation:

Step1: Find GCF of coefficients

Factors of 28: $1,2,4,7,14,28$; Factors of 49: $1,7,49$; Factors of 35: $1,5,7,35$. GCF is $7$.

Step2: Check common variables

Terms: $28vw$ (variables $v,w$), $49v$ (variable $v$), $35w$ (variable $w$). No common variable across all terms.

Step3: Verify GCF of polynomial

Since there is no common variable, GCF is $7$, not $7v$.

Step4: Check factoring format

Each term as product with GCF: $7(4vw) + 7(7v) + 7(5w)$, not $7(28vw)+7(49v)+35(w)$.

Step5: Verify factored expression

Factor out $7$: $7(4vw + 7v + 5w)$.

Answer:

• There are no common variables among all three terms.
• The resulting expression when factoring out the GCF is $7(4vw + 7v + 5w)$.