## EmmaH Group Title Solve by factoring: 3x^2 + 2x - 1 = 0 {-1, 2/3} {1, -2/3} {-1, 1/3} {1, -1/3} one year ago one year ago

1. EmmaH

please explain how i find this

2. JamesJ

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

3. Hero

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

4. EmmaH

divide what by three?

5. Hero

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

6. EmmaH

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

7. Hero

Okay, now what's the next step?

8. Hero

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

9. EmmaH

3x(1x+1)

10. Hero

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

11. EmmaH

?

12. JamesJ

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) ?

13. EmmaH

what do you mean?