If the length of a rectangle is x-2 and its area is 2x^3 - 8x^2 + 2x + 12, SHOW how to determine the rectangle's width.

2x^2 - 4x - 6. This is the width of the rectangle.

Step-by-step explanation:

This can be solved using long division or synthetic division. Both are ways of dividing polynomials.

Synthetic: find the divisor from x-2, which is 2 since x - k is the proper form.

The remaining numbers come from our coefficients and constant in the polynomial.

Drop the first constant, multiply by the divisor and add the two values.

Drop the first 2; 2 x 2 = 4 which is added to - 8 to get - 4. Repeat.

2| 2 - 8 2 12

4 - 8 - 12

2 - 4 - 6 0

Now we reform the polynomial from this. 2x^2 - 4x - 6. This is the width of the rectangle.