SOLUTION: The volume of a box is given by V = 2x^3 - 11x^2 + 10x + 8. Find an expression for the missing dimension. Length = 2x + 1 Face Area= x - 4 * ? What I have so far is: V =

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Question 948617: The volume of a box is given by V = 2x^3 - 11x^2 + 10x + 8. Find an expression for the missing dimension.
Length = 2x + 1
Face Area= x - 4 * ?
What I have so far is:
V = 2x + 1 * x - 4 * ?
Which is:
2x^3 - 11x^2 + 10x + 8 = 2x + 1 * x - 4 * ?
I used synthetic division to divide V by x - 4 and got 2x^2 - 3x - 2
Then I used polynomial long division to divide that by 2x + 1 and got x + 2
However the answer key says it is x - 2 not x + 2.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Find an expression for width multiplied by height using polynomial division for . In other words, L for length, w for width, h for height,
. You could expect wh is a factorable quadratic expression.



Polynomial Division for V/L:

__________________x^2_______-6x________8________---------------------quotient line
____________|________________________________________
____________|
____________|_____2x^3_____-11x^2______10x________8----------------dividend line
2x+1________|
____________________________________________________
__________________2x^2_____x^2
________________________________
_________________0________-12x^2______10x
__________________________-12x^2_____-6x
____________________________________________
___________________________0_________16x_________8
_____________________________________16x_________8
____________________________________________________
_____________________________________0__________0----------------shows any remainder

The division operation indicates .

w*h, an area, may be factorable.
, an area expression.

Not in any particular order, the dimensions OTHER THAN L are (x-2) and (x-4).
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

The volume of a box is given by V = 2x^3 - 11x^2 + 10x + 8. Find an expression for the missing dimension.
Length = 2x + 1
Face Area= x - 4 * ?
What I have so far is:
V = 2x + 1 * x - 4 * ?
Which is:
2x^3 - 11x^2 + 10x + 8 = 2x + 1 * x - 4 * ?
I used synthetic division to divide V by x - 4 and got 2x^2 - 3x - 2
Then I used polynomial long division to divide that by 2x + 1 and got x + 2
However the answer key says it is x - 2 not x + 2.
Since you already have 2 dimensions, you can multiply them to get the DIVISOR

Thus, 

We then proceed by dividing  by 

                        x - 2                                  
2x^2 - 7x - 4 ) 2x³ - 11x² + 10x   +   8
                       2x³ -  7x²  -   4x
                             -  4x² + 14x   +   8
                              - 4x² + 14x   +   8

As seen, the quotient is:     

You can do the check!! 

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