The area of a rectangle is represented by the function x3 − 2x2 − 40x − 64. The width of the rectangle is x + 4. Find the expression representing the length of the rectangle.

A. x2 − 8x − 20
B. x2 + 12x + 20
C. x2 − 6x − 16
D. x2 + 10x + 16

Step-by-step explanation:

If the area is

and area = length * width and our width is given as x + 4, then the length is found by dividing the area by the width.  You could do that using long division, but it's easier using synthetic division.

-4 |   1   -2   -40   -64

    ______________

       1

This is how you start.  The -4 inside the box comes from the factor you are dividing by.  If x + 4 = 0, then x = -4.  The numbers after are the coefficients from each descending power of x.  Multiply the -4 by the 1 and put that product up under the -2 and add to get:

-4 |   1   -2   -40   -64

            -4

--------------------------------

       1     -6

Now multiply -4 by -6 and put that product up under the -40 and add:

-4 |  1    -2  -40   -64

           -4   24

   -------------------------

      1    -6    -16

Multiplying -4 by -16 gives you 64 so when you add you get a remainder of 0.

The numbers under the line give you the depressed polynomial

That gives you the expression for the length.  That's C.        

answer

the correct answer is

explanation

the given function is

the excluded values are obtained by solving:

we factor to obtain:

the excluded values are

the answer is 1030 it's very simple math.