Which statement is correct about the function y = 3x2 + 19x – 14?
a) in factored form, the function is y = (3x – 2)(x + 7), so the zeros of the function are x = -7 and x = 2 3 .
b) in factored form, the function is y = (3x + 2)(x – 7), so the zeros of the function are x = -7 and x = 2 3 .
c) in factored form, the function is y = (3x – 2)(x + 7), so the zeros of the function are x = 7 and x = - 2 3 .
d) in factored form, the function is y = (3x + 2)(x – 7), so the zeros of the function are x = 7 and x = - 2 3 .

You just have to factor the given expression. You do this by factoring the first term and the last term.

3 can only be factored with 3x • x, so let's put that into our parentheses.

(3x ?)(x ?)

Now the last term. -14 can be factored more ways than one. Here are some examples:

-14 • 1
14 • -1
7 • -2
-7 • 2

We know we can't use the first two since they're not options in this question. We also know the middle term is something quite large, so that number is what should be multiplied by three.

(3x - 2)(x + 7)

Let's test it out. By multiplying the insides, the outsides, and adding them together. 

-2 • x = -2x

7 • 3x = 21x

21x - 2x = 19x

Aha! That is correct! Now that we've gotten that figured out, we can eliminate B and D. But what about the others? Well, I usually just graph out the factors with a calculator and see the zeroes from there, but since I don't have that luxury in this case. I'll have to find out some other way. I would say to multiply the factors by each other and switch the signs (without the x).

7 = -7

-2 x 3 = -

- =

That should be your answer. If you have any questions, let me know.