Question

mial equations: practice
question 1 of 5
select the correct answer.
which function has zeros at -2, -1, and 4?
$f(x)=(x - 2)(x - 1)(x + 4)^2$
$f(x)=(x + 2)(x + 1)(x + 4)$
$f(x)=(x + 2)^2(x + 1)(x - 4)$
$f(x)=x(x - 2)(x - 1)(x - 4)$

Explanation:

Step1: Recall zero-product property

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

Step2: Create factors from given zeros

For zeros $x=-2$, $x=-1$, $x=4$, the factors are $(x+2)$, $(x+1)$, $(x-4)$.

Step3: Match factors to options

Check which option contains all three factors. Option 3 has $(x+2)^2$, $(x+1)$, $(x-4)$, which includes the required factors (the squared term only creates a repeated zero at -2, which still counts as a zero of the function).

Answer:

C. $f(x)=(x+2)^2(x+1)(x-4)$