Algebra II help. Am I Correct?

Question

Which of the following polynomials has -2,-3, and -4 as zeros?

I. P(x) = (x - 2)(x - 3)(x - 4)
II. P(x) = (x + 2)(x + 3)(x + 4)
III. P(x) = -2(x - 2)(x - 3)(x - 4)



1) I only

2) II only

3) I and III only

4) I, II, and III

 

 

I think its #4 

If I'm wrong please explain

thank you

Answer 1

# 2 is correct.  Set the polynomial equal to zero; since it's in factored form, you use the Zero Product Property:

the only way any product can be zero is for any of its factors to be zero, separately.  Thus x+2 = 0 leads you to the solution x = -2.  Similarly for the other factors.