14. Factor the polynomial by grouping, if possible.

3v2w - 21vw - 3v2 + 21v

A. 3vw (v - 7) - 3 (w - 1)

B. 3v (v - 7) (w - 1)

C. It can't be factored.

D. 3v (v - 7) (v + 1)

3 v (v - 7) (w - 1) thus the answer is B:

Step-by-step explanation:

Factor the following:

3 v^2 w - 21 v w - 3 v^2 + 21 v

Factor 3 v out of 3 v^2 w - 21 v w - 3 v^2 + 21 v:

3 v (v w - 7 w - v + 7)

Factor terms by grouping. v w - 7 w - v + 7 = (v w - 7 w) + (7 - v) = w (v - 7) - (v - 7):

3 v w (v - 7) - (v - 7)

Factor v - 7 from w (v - 7) - (v - 7):

Answer: 3 v (v - 7) (w - 1)