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Factor the polynomial given that f(k) = 0

x^3 - 5x^2 - 2x + 24; k = -2


I'm hoping somebody can explain how to figure out one of these problems.

User Kelz
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1 Answer

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Answer:

The following polynomial can be factorized as,

f(x) =
(x-4)(x-3)(x+2)

Explanation:

It is given that at x = -2, the value of polynomial is zero, thus, by factor theorm,

(x+2) is the factor of the above polynomial.

By dividing the given polynomial by (x+2), we get,

F(x) =
(x-4)(x^(2) -7x +12)

This can be further simplified as,


(x^(2) -7x +12) =
(x^(2) -4x-3x+12)

=
(x(x-4)-3(x-4))=
(x-3)(x-4)

Thus the polynomial becomes,

f(x) =
(x-4)(x-3)(x+2)

User Nbsrujan
by
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