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.
<pre><font face = "Tohoma" size = 4 color = "indigo"><b>Since you already have 2 dimensions, you can multiply them to get the DIVISOR

Thus, {{{(2x + 1)(x - 4) = 2x^2 - 7x - 4}}}

We then proceed by dividing {{{2x^3 - 11x^2 + 10x + 8}}} by {{{2x^2 - 7x - 4}}}

                        x - 2                                  
2x^2 - 7x - 4 <span style="text-decoration: overline">) 2x³ - 11x² + 10x   +   8</span>
                       <u>2x³ -  7x²  -   4x</u>
                             -  4x² + 14x   +   8
                             <u> - 4x² + 14x   +   8</u></pre>
<pre>As seen, the quotient is: {{{highlight_green(x - 2)}}}    
You can do the check!! 
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