Question

find an equation of a degree 3 polynomial (in factored form) with the given zeros of $f(x)$: $3, -3, 4$. assume the leading coefficient is 1.
$f(x) = \square$
question help: video read written example

Explanation:

Step1: Use zero-factor theorem

If $r$ is a zero, $(x-r)$ is a factor.
Factors: $(x-3)$, $(x-(-3))=(x+3)$, $(x-4)$

Step2: Multiply factors for polynomial

Since leading coefficient is 1, multiply the factors directly.
$f(x) = (x-3)(x+3)(x-4)$

Answer:

$f(x)=(x-3)(x+3)(x-4)$