Which of the following could be a function with zeros of -3 and 2? a. f(x)=(x-3)(x+2) b. f(x)=(x-3)(x-2) c. f(x)=(x+3)(x-2) d. f(x)=(x+3)(x+2)

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Given zeros are x=-3 and x=2. Now we have to find which of the given function will satisfy the given zeros. To find that we will just plug x=-3 and x=2 to see which choice gives output 0 for both.

Test for A. f(x)=(x-3)(x+2)

f(-3)=(-3-3)(-3+2)=(-6)(-1)=6

Output is not 0 so this can't be the answer.

Test for B.f(x)=(x-3)(x-2)

f(-3)=(-3-3)(-3-2)=(-6)(-5)=30

Output is not 0 so this can't be the answer.

Test for C.f(x)=(x+3)(x-2)

f(-3)=(-3+3)(-3-2)=0(-5)=0

f(2)=(2+3)(2-2)=(5)(0)=0

Output is 0 so this is the answer.

Test for D.f(x)=(x+3)(x+2)

f(-3)=(-3+3)(-3+2)=(0)(-1)=0

f(2)=(2+3)(2+2)=(5)(4)=20

Output is not 0 so this can't be the answer.

Hence final answer is C.f(x)=(x+3)(x-2)

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step-by-step explanation: