EmmaH
Solve by factoring: 3x^2 + 2x - 1 = 0
{-1, 2/3}
{1, -2/3}
{-1, 1/3}
{1, -1/3}
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EmmaH
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please explain how i find this
JamesJ
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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
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@EmmaH, the steps for solving this are the same as what I showed you in the previous problem.
EmmaH
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divide what by three?
Hero
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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
EmmaH
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(3x^2+3x) + (-1x-1)?
Hero
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Okay, now what's the next step?
Hero
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Do you know how to factor \(3x^2 + 3x\) ?
EmmaH
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3x(1x+1)
Hero
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Yes, or simply 3x(x + 1)
Writing 1 before the x is not necessary.
Now factor (-1x - 1). Let me know what you get.
EmmaH
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?
JamesJ
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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) ?
EmmaH
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what do you mean?