The polynomial of degree 4, P ( x ) has a root of multiplicity 2 at x = 4 and roots of multiplicity 1 at x = 0 and x = − 4 . It goes through

Question

The polynomial of degree 4, P ( x ) has a root of multiplicity 2 at x = 4 and roots of multiplicity 1 at x = 0 and x = − 4 . It goes through the point ( 5 , 36 ) . Find a formula for P ( x ) . You may give the answer is factored form.

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Natalia 7 days 2021-11-22T06:08:53+00:00 1 Answer 0 views 0

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    2021-11-22T06:10:43+00:00

    Answer: P(x) = {(x-4)^2} (x) (x+4)

    Step-by-step explanation:

    Let’s start with the multiplicity of 2;

    At multiplicity of 2; x=4.

    Therefore, x – 4 is a factor of the function P(x).

    Since it has a multiplicity of 2, we will rewrite the factor as (x-4)^2

    Now for the multiplicity of 1.

    At this multiplicity of 1, x= 0 and – 4.

    Therefore, the factors are x-0 and x+4

    Since multiplicity of 1, the factors remain as they are without any additional root on top.

    Therefore, the factors of the polynomial p(x) are (x-4)^2 and x and x+4.

    And solution of P(x) in factor form will be: P(x) = {(x-4)^2} (x) (x+4)

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45:7+7-4:2-5:5*4+35:2 =? ( )