Question

select the correct answer.
which function represents a function with zeros at -3, -1, 0, and 6?
a. $y=(x - 6)(x + 1)(x + 3)$
b. $y=x(x - 3)(x - 1)(x + 6)$
c. $y=x(x - 6)(x + 1)(x + 3)$
d. $y=(x - 3)(x - 1)(x + 6)$

Explanation:

Step1: Recall zero-product property

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

Step2: Write factors for each zero

• Zero at $-3$: $(x-(-3))=(x+3)$
• Zero at $-1$: $(x-(-1))=(x+1)$
• Zero at $0$: $(x-0)=x$
• Zero at $6$: $(x-6)$

Step3: Multiply all factors

$y = x(x-6)(x+1)(x+3)$

Step4: Match to options

Compare with given choices.

Answer:

C. $y = x(x - 6)(x + 1)(x + 3)$