Question

A rectangle has an area of x^3+x^2-7x+2 square meters and a width of x-2 meters. Find its length.

Answer 1

$\bf \textit{area of a rectangle}=A=length\times width\implies \cfrac{A}{width}=length \\\\\\ thus\quad \begin{cases} A=x^3+x^2-7x+2\\ width=x-2 \end{cases}\implies \cfrac{x^3+x^2-7x+2}{x-2}=length$

hint:  divisor is x-2 form, thus you can use syntheric division