Question 206449: I am studying for the compass exam and I see that others have posted the same question: What is the rational expression when r is not equal to plus or minus 2, r^2-5r+6 / r^2-4. What I don't understand is why r^2-5r+6 factors to [(r-3)(r-2)]...please help!
Found 2 solutions by stanbon, RAY100:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! You first learn to multiply: 2*3=6
Then you learn to factor: 6=2*3
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Your problem:
What I don't understand is why r^2-5r+6 factors to [(r-3)(r-2)]...
You first learn FOIL:
(r-3)(r-2)
F: r*r = r^2
O: r*-2= -2r
I: -3*r= -3r
L: -2*-3= 6
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Then you learn to factor:
r^2-5r+6
Think of two numbers whose product is 6 and whose sum is -5
The numbers are -2 and -3
Rewrite the problem replacing -5r by -3r-2r
r^2-3r-2r+6
Factor the 1st two and the last two terms separately:
r(r-3)-2(r-3)
Factor again to get the factored answer:
(r-3)(r-2)
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Hope that helps.
Cheers,
Stan H.
Answer by RAY100(1637) (Show Source):
You can put this solution on YOUR website! r^2 -5r +6
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Remember factoring is reverse FOIL
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factors of first term are only 1*1,,,,,(x,,,,)(x,,,,,)
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sign of last term is plus, therefore both terms of factor must be the same,,,and the sign of the middle term is negative, therefore both factors have negative,,,,,that is ( x-,,)(x-,,)
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factors of last term can be,,6*1,,3*2,,,,but which adds to 5 which is middle term,,,must be 3*2,,
Therefore,,,,(x-3)(x-2) are the factors of x^2 -5x +6
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to check use FOIL, (x-3)(x-2) = x^2 -2x -3x +6 = x^2 -5x +6
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