Algebra 2 polynomials as zeros?

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

Answer 1

Every zero must come from a factor when the polynomial is set equal to zero to solve for them.

 

If -2 is a zero, then x - (-2) = x + 2 must be a factor. Similarly, (x + 3) and (x + 4) are factors.

 

When you multiply these three factors together, you get the polynomial up to a constant multiple.

 

The correct answer is II.