Question

Factor the following expression completely given that one of the factors is (w − 7):

w^3 − 12w^2 + 29w + 42 =

Answer 1

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

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

Answer 2

(w-7(w+1)(w-6)

Explanation:

given that one of the factors is (w − 7)

Divide the given expression by w-7

Use long division

w^2 -5w - 6

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w-7 w^3 − 12w^2 + 29w + 42

(-)w^3 - 7w^2

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-5w^2 + 29w

(-)-5w^2 + 35 w

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-6w + 42

(-) -6w + 42

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0

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Now we factor the quotient w^2 -5w - 6

`w^2 -5w - 6`

We need two factors whose sum is -5 and product is -6

-6 and 1 gives us sum -5 and product -6

`(w-6)(w+1)`

`w^3 - 12w^2 + 29w + 42 = (w-7(w+1)(w-6)`