Question

find a polynomial f(x) of degree 5 that has the following zeros.
4, -9 (multiplicity 2), -6, 7
leave your answer in factored form.
f(x) =

Explanation:

Step1: Use zero-factor theorem

For a zero $a$, the factor is $(x-a)$.

Step2: Account for multiplicity

For zero $-9$ (multiplicity 2), factor is $(x+9)^2$.

Step3: Combine all factors

Multiply factors for all zeros.
$f(x) = (x-4)(x+9)^2(x+6)(x-7)$

Answer:

$f(x) = (x-4)(x+9)^2(x+6)(x-7)$