Question

find a polynomial $f(x)$ of degree 4 that has the following zeros.
1, -7, 0, -5
leave your answer in factored form.
$f(x)=\square$

Explanation:

Step1: Use zero-factor theorem

If $r$ is a zero, $(x-r)$ is a factor.

Step2: List factors for each zero

For zero $1$: $(x-1)$; for $-7$: $(x-(-7))=(x+7)$; for $0$: $(x-0)=x$; for $-5$: $(x-(-5))=(x+5)$

Step3: Multiply all factors

$f(x) = x(x-1)(x+7)(x+5)$

Answer:

$f(x) = x(x-1)(x+7)(x+5)$