SOLUTION: The polynomial 4x3 − 38x2 + 90x gives the volume (in cubic inches) of the resulting box when a square with sides x inches long is cut from each corner of a 9 in. × 10 in. pi

Algebra ->  Equations -> SOLUTION: The polynomial 4x3 − 38x2 + 90x gives the volume (in cubic inches) of the resulting box when a square with sides x inches long is cut from each corner of a 9 in. × 10 in. pi      Log On


   

Question 1196708: The polynomial
4x3 − 38x2 + 90x
gives the volume (in cubic inches) of the resulting box when a square with sides x inches long is cut from each corner of a 9 in. × 10 in. piece of cardboard. Find the volume of a box if 2-inch squares are cut out.
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
2%289-2%2A2%29%2810-2%2A2%29, the volume in cubic inches
2%285%29%286%29

That equal to 4x%5E3-38x%5E2%2B90x=2%2A5%2A6
2x%5E3-19x%5E2%2B45x=5%2A6
2x%5E3-19x%5E2%2B45x-30=0

One root is x=2, if try Rational Roots Theorem. 
2    |    2    -19    45    -30
     |
     |           4   -30     30
     |________________________________
         2     -15     15      0

So the equation can be rewritten
%282x%5E2-15x%2B15%29%28x-2%29=0
and general quadratic equation solution will help for roots of the quadratic factor.

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.

All you need is to substitute x= 2 into the given function, and calculate the value

    V(2) = 4*2^3 - 38*2^2 + 90*2 = 4*8 - 38*4 + 90*2 = 60 cubic inches.    ANSWER

Solved.


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
The polynomial
4x3 − 38x2 + 90x
gives the volume (in cubic inches) of the resulting box when a square with sides x inches long is cut from each corner of a 9 in. × 10 in. piece of cardboard. Find the volume of a box if 2-inch squares are cut out.
Length of each side of each cut-out square/Height of box: 2"

Length of cardboard before squares were cut out: 10" 
Length of cardboard after squares were cut out/Length of base of box: 10 - 2(2) = 10 - 4 = 6"

Width of cardboard before squares were cut out: 9" 
Width of cardboard after squares were cut out/Width of box: 9 - 2(2) = 9 - 4 = 5"

Volume of box formed after squares were cut out from cardboard: LWH = 6(5)(2) = 60 cubic inches

OR

Substitute 2 for x in volume-polynomial: 4x3 − 38x2 + 90x.