Need help with Algebra 2 problem.

Question

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

I. P(x) = x² + x - 6
II. P(x) = x² - x - 6
III. P(x) = 2x² + 2x - 12

1) I only

2) II only

3) I and III

4) I, II, and III

 

I don't understand. Please explain. Thank you.

Answer 1

Hi Terry.

 

Let's factor each of the polynomials listed.  Then set the factors equal to zero and solve for x

 

 

I

x²+x-6

(x+3)(x-2) = 0

x+3 = 0     x-2=0

x = -3, 2

So I has the right zeros

 

II x²-x-6
(x-3)(x+2) = 0
x-3 = 0 x+2=0
x = 3, -2
So II does not have the right zeros

 

III   2x² + 2x - 12

2(x² + x - 6) = 0

2(x+3)(x-2) = 0

x+3 = 0     x-2 = 0

x = -3, 2

III does have the right zeros

 

 

I and III;  the correct answer is 3)