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

Coefficients are 28, 49, 35. Prime factors:
$28=2^2 \times 7$, $49=7^2$, $35=5 \times 7$. GCF is $7$.

Step2: Check common variables

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

Step3: Evaluate each statement

1. "Coefficients have no common factors other than 1": False (GCF is 7).
2. "No common variables among all terms": True (no variable present in all 3 terms).
3. "GCF of the polynomial is $7v$": False (no common variable $v$ in all terms).
4. "Each term as product with GCF: $7(28vw)+7(49v)+7(35w)$": False (this multiplies to $7 \times$ original, not equal to original).
5. "Factored out GCF: $7(4vw + 7v + 5w)$": True (since $7 \times 4vw=28vw$, $7 \times 7v=49v$, $7 \times 5w=35w$).

Answer:

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