• anonymous
Which of the following shows the factors of 9x^2+3x-2? (9x-2)(x+1) is this correct?
  • Stacey Warren - Expert
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  • chestercat
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  • FortyTheRapper
No, (9x-2)(x+1) factors out to 9x^2+7x-2 This one doesn't look like it would factor
  • whpalmer4
You can test your factoring by multiplying it out: \[(9x-2)(x+1) = 9x*x + 9x*1 -2*x -2*1 = 9x^2+7x-2\]That is not what you factored, so it is not correct. It is possible to factor this expression, however: \[9x^2+3x-2\]There aren't any common factors that we can factor out. However, we can factor the \(9x^2\) term in a few ways: \(3x*3x\) is an obvious choice, let's see if it can be made to work: \[(3x + a)(3x + b) = 9x^2 +3x- 2\]If we expand our left hand side: \[(3x+a)(3x+b) = 3x*3x + 3x*b + a*3x + a*b\]\[9x^2 + (3a+3b)x + ab\] Compare that with our original: \[9x^2 + (3a+3b)x + ab = 9x^2 + 3x - 2\]If we can pick values of \(a,b\) that make \((3a+3b) = 3\) and \((ab) = -2\) then we are done. Easier to crack the \(ab = -2\), I think. Our choices are -1*2 and -2*1. Don't know which yet, but let's try those two in the second one:\[(3a+3b) =3\] \[3(-2)+3(1) = -6+3 = -3\]okay, \(a=-2,b=1\) is not it \[3(-1) + 3(2) = 3\]\[-3+6 = 3\]So that works. Plug \(a=-1,\ b=2\) back into our prototype factored equation: \[(3x+a)(3x+b) =(3x-1)(3x+2)\] Let's multiply to make sure it is correct: \[(3x-1)(3x+2 = 3x*3x + 3x*2 -1*3x -1*2 = 9x^2 +6x-3x-2\]\[ = 9x^2+3x-2\checkmark\]
  • anonymous
Thank you!

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