factoring a difference or sum of two cubes

[traceylsambrose]

your help is greatly appreciated;
Each of the three demensions of a cube with a volume of y3 cubic centimeters is decreased by a whole numberb of centimeters. If the new volume is y3 - 13y2 + 54y - 72 cubic centimeters and the new width is y-6 centimeters, then what are the the new length and height?

Thank you in advance - Tracey

 

[tkhunny]

You are given one of the factors. Have you seen Synthetic Division?

Quick hint: 72 = 6*12 = 6*(1*12) = 6*(2*6) = 6*(3*4) -- There are only a few possibilities.

 

[steve_b]

Each of the three demensions of a cube with a volume of y3 cubic centimeters is decreased by a whole numberb of centimeters. If the new volume is y3 - 13y2 + 54y - 72 cubic centimeters and the new width is y-6 centimeters, then what are the the new length and height?

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Since you have the volume and one side, you can find the product of the other two sides by doing the polynomial long division:

y^3 - 13y^2 + 54y - 72
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y - 6

This will give a quotient of:

y^2 - 7y + 12

which factors into:

(y - 4)(y - 3)

Hope that helps...

Steve