Answer:
(w-7(w+1)(w-6)
Step-by-step explanation:
given that one of the factors is (w − 7)
Divide the given expression by w-7
Use long division
w^2 -5w - 6
-------------------------------------
w-7 w^3 − 12w^2 + 29w + 42
(-)w^3 - 7w^2
-------------------------------------------
-5w^2 + 29w
(-)-5w^2 + 35 w
----------------------------------------------------
-6w + 42
(-) -6w + 42
--------------------------------------------------
0
--------------------------------------------------
Now we factor the quotient w^2 -5w - 6
[tex]w^2 -5w - 6[/tex]
We need two factors whose sum is -5 and product is -6
-6 and 1 gives us sum -5 and product -6
[tex](w-6)(w+1)[/tex]
[tex]w^3 - 12w^2 + 29w + 42 = (w-7(w+1)(w-6)[/tex]
Answer:
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
