Factor the following expression completely given that one of the factors is (w − 7): w^3 − 12w^2 + 29w + 42 =

The factors of w^3 − 12w^2 + 29w + 42 are (w -7), (w-6) and (W + 1 )

Step-by-step explanation:

It is given that (w − 7) is one factor of w^3 − 12w^2 + 29w + 42

When we divide w^3 − 12w^2 + 29w + 42 by w-7 we get the quotient W^2 – 5w -6 and remainder 0

Therefore

w^3 − 12w^2 + 29w + 42 can be written as,

w^3 − 12w^2 + 29w + 42 = (w -7)(W^2 – 5w -6 )  

When we factorize W^2 – 5w -6 we get

W^2 – 5w -6 = (w+1)(w-6)

Therefore,

The factors of w^3 − 12w^2 + 29w + 42 are (w -7), (w-6) and (W + 1 )  

The long division method is attached  with this answer