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.

Answer 1

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)