How to form a polynomial with given zeros and degree and multiplicity calculator

Taking P (x) = x³-12x-16 as an example

Step-by-step explanation:

For a polynomial, if

x = a is a zero of the function, then (x - a) is a factor of the function.

We have two unique zeros:

-2 and 4. However, - 2 has a multiplicity of 2, which means that the factor that correlates to a zero of - 2 is represented in the polynomial twice.

Following how it's constructed

zero at - 2, multiplicity 2

zero at 4, multiplicity 1

p (x) = x - (-2)) ² (x-4) ¹

Thus, p (x) = (x+2) ² (x-4)

Expand: p (x) = (x²+4x+4) (x-4)

p (x) = x³-12x-16