The area of a rectangle is x³ - 8x² + 7 and one of its sides is x - 1. Find the length of the adjacent side.

Area of the rectangle = x³ - 8x² + 7

One side = (x - 1)

As we know the area of rectangle = One side x Other side

Other side = Area of rectangle ÷ One side

= (x³ - 8x² + 7) ÷ (x - 1)

$\begin{array}{l} \phantom{x - 1)}{x^2 - 7x - 7} \ x - 1\overline{\smash{\big)}x^3 - 8x^2 + 7} \ \phantom{x - 1}\underline{\underset{-}{}x^3 \underset{+}{-}x^2} \ \phantom{{x - 1}12x}-7x^2 + 7 \ \phantom{{x - 1}221x}\underline{\underset{+}{-}7x^2 \phantom{+ 7} \underset{-}{+} 7x} \ \phantom{{x - 1}{2x^3+}{+5x}}-7x + 7 \ \phantom{{x - 1}{2x^3+}{+5x^2}}\underline{\underset{+}{-}7x \underset{-}{+} 7} \ \phantom{{x - 1}{2x^3+}{+5x^2}{-7x}} \times \end{array}$

Hence, length of adjacent side is x² - 7x - 7.