Question

Find a polynomial f (x) of degree 3 that has the following zeros.6 (multiplicity 2), -7Leave your answer in factored form.

Answer 1

If a polynomial has a zero of "a" with multilicity b, the factor would be:

`(x-a)^b`

So, accordingly the factors would be:

`\begin{gathered} (x-6)^2 \\ (x-(-7))^1 \end{gathered}`

They are

`\begin{gathered} (x-6)^2 \\ (x+7) \end{gathered}`

We can write out the polynomial, f(x), as:

`f(x)=(x-6)^2(x+7)`