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Question 245039: How would I factor a problem like 8xsquared - 4x - 20, and the checkit by multiplying it?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! How would I factor a problem like 8xsquared - 4x - 20, and the checkit by multiplying it?
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Look for a common factor:
8x^2 - 4x - 20
4(2x^2-x-5)
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Use the quadratic formula on 2x^2-x-5:
x = [1 +- sqrt(1-4*2*-5)]/4
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x = [1 +- sqrt(41)]/4
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Roots: (1+sqrt(41))/4 ; (1-sqrt(41))/4
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Factors: 4 ; x - [1/4 + (1/4)sqrt(41)] ; x - [1/4 -(1/4)sqrt(41)]
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Checking:
4[(x-(1/4)-(1/4)sqrt(41)][(x-(1/4)) + (1/4)sqrt(41)]
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= 4[(x-(1/4))^2 - ((1/4)sqrt(41))^2]
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= 4[x^2 - (1/2)x + 1/16 - [(1/16)*41]]
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= 4[x^2 - (1/2)x - (40/16)]
= 4x^2 - 2x -10
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Cheers,
Stan H.
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