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2 October, 02:03

Find a polynomial function of degree 3 such that f (2) = 24 and x - 1, x and x + 2

are factors of the polynomial.

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  1. 2 October, 05:13
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    f (x) = 3x³ + 3x² - 6x

    given the factors of the polynomial, then

    f (x) = ax (x - 1) (x + 2) (a is a multiplier)

    to find a use f (2) = 24

    f (2) = 2a (1) (4) = 24 ⇒8a = 24 ⇒ a = 3, thus

    f (x) = 3x (x² + x - 2) = 3x³ + 3x² - 6x
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