Question

write a cubic function f(x) that has a constant factor of 2 and these zeros: x = 0, x = 3i, x = -3i. enter the answer in the space provided. use numbers instead of words. f(x)=\boxed{}

Explanation:

Step1: Form factor from zeros

If $x=a$ is a zero, then $(x-a)$ is a factor. So the factors from zeros $x=0$, $x=3i$, $x=-3i$ are $x$, $(x-3i)$, $(x+3i)$. Multiply by constant factor 2:
$f(x)=2x(x-3i)(x+3i)$

Step2: Multiply complex factors

Use difference of squares: $(x-3i)(x+3i)=x^2-(3i)^2$. Since $i^2=-1$, we get:
$x^2-(3i)^2=x^2-9(-1)=x^2+9$

Step3: Multiply remaining terms

Multiply $2x$ with $(x^2+9)$:
$2x(x^2+9)=2x^3+18x$

Answer:

$2x^3+18x$