which statements are true about the polynomial (28vw + 49v+35w)? check all that apply.\nthe coefficients…

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

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

Answer

Explanation:

Step1: Analyze coefficients

Coefficients: (28 = 2^2\times7), (49 = 7^2), (35=5\times7). GCF of coefficients is (7).

Step2: Analyze variables

Terms: (28vw), (49v), (35w). No common variable in all three terms.

Step3: Check GCF of polynomial

Since no common variable in all terms, GCF is (7) (not (7v)).

Step4: Check term - product form

(28vw=7\times4vw), (49v = 7\times7v), (35w=7\times5w). Correct form is (7(4vw)+7(7v)+7(5w)).

Step5: Check factored form

Factor out (7): (28vw + 49v+35w=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)).