Solve by factoring: 3x^2 + 2x - 1 = 0
{-1, 2/3}
{1, -2/3}
{-1, 1/3}
{1, -1/3}

Question

Solve by factoring: 3x^2 + 2x - 1 = 0 
    {-1, 2/3} 
   {1, -2/3} 
   {-1, 1/3} 
   {1, -1/3}

anonymous · Answer

please explain how i find this

jamesj · Answer

well, dividing first by 3, we have

$$ x^2 + \frac{2}{3}x - \frac{1}{3} = 0 $$
Now, you want factors of -1/3 that add up to 2/3

hero · Answer

@EmmaH, the steps for solving this are the same as what I showed you in the previous problem.

anonymous · Answer

divide what by three?

hero · Answer

I'll even give you a hint, but you have to solve the rest yourself:

Given:
$3x^2 + 2x - 1$

Split the middle term:
$3x^2 + 3x - 1x - 1$

Now factor by grouping

anonymous · Answer

(3x^2+3x) + (-1x-1)?

hero · Answer

Okay, now what's the next step?

hero · Answer

Do you know how to factor $3x^2 + 3x$ ?

anonymous · Answer

3x(1x+1)

hero · Answer

Yes, or simply 3x(x + 1)

Writing 1 before the x is not necessary. 

Now factor (-1x - 1). Let me know what you get.

anonymous · Answer

?

jamesj · Answer

Well, you have a factor of (x+1) above where you wrote
3x(x+1)

Can you get a factor of (x+1) out of (-1x - 1) ?

anonymous · Answer

what do you mean?