Question

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

Answer 1

Answer:

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