Question

How do you write a polynomial whose zeros are -9, multiplicity of 1, 4 multiplicity of 2 and degree 3?

Answer 1

`f(x)=(x+9)(x-4)^2`

Explanation:

A zero of `-9` with a multiplicity of `1` tells us that `(x+9)` is a factor of our polynomial.

The multiplicity of a zero simply tells us how many times the factor involving that zero shows up. A zero of `4` with a multiplicity of `2` tells us that `(x-4)(x-4)=(x-4)^2` is another factor of our polynomial. Since the multiplicity is `2`, it must show up twice.

So, we obtain

`f(x)=(x+9)(x-4)^2`

This is indeed of degree `3` -- if we multiplied everything out, the leading term would be `x^3`, the term of the highest exponent in the polynomial, making it `3rd` degree.