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Write a polynomial equation, P ( x ) , in factored form given the following requirements: Degree: 4 Leading coefficient 1 Three of the zeros are at x = 1 , x = − 4 and x = 2 y -intercept at ( 0 , − 24 ) Note: P ( x ) written in factored form means it is written as a product of its factors.



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Step-by-step explanation:

P(x) = (x - 1)(x - 2)(x + 4)(x - a) where a is an integer to be found.

The y intercept occurs when x = 0, so substituting for x:-

(0 - 1)(0 - 2)(0 + 4)(0 - a) = -24

---> 8(0 - a) = -24

---> -8a = -24

---> a = 3

So, the required polynomial is

P(x) = (x - 1)(x - 2)(x - 3)(x + 4)

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