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

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).

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).

Answer

Explanation:

Step1: Analyze coefficients

Find the GCF of 28, 49, and 35. Prime - factorize: (28 = 2\times2\times7), (49 = 7\times7), (35 = 5\times7). The GCF of 28, 49, and 35 is 7.

Step2: Analyze variables

The first term is (28vw), the second term is (49v), and the third term is (35w). There is no variable common to all three terms.

Step3: Determine GCF of polynomial

The GCF of the polynomial (28vw + 49v+35w) is 7 since there is no common variable among all terms and the GCF of coefficients is 7.

Step4: Factor out GCF

Factor out 7 from each term: (28vw+49v + 35w=7(4vw + 7v+5w)).

Answer:

The statements that are true are:

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