1. A rectangle has an area of x3 + x2 – 7x + 2 square meters and a width of x – 2 meters. Find its length.

Answer 1

ah ha, so this is why you want to divide polynomials
*******______ x^2____________________
(x-2) | x^3 + x^2 - 7 x + 2
********x^3 -2 x^2
********--------------------
************+3 x^2 - 7 x + 2

*******______ x^2_+3x__-1____
(x-2) | x^3 + x^2 - 7 x + 2
********x^3 -2 x^2
********--------------------
************+3 x^2 - 7 x + 2
************+3 x^2 -6 x
************----------------
******************* -1 x + 2
******************* -1 x + 2
*******************-----------
**********Remainder = 0
so
x^2 +3 x - 1