Question

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

Answer 1

Area = x³ − 8x + 7

One side = x − 1

∴ Adjacent side = (x³ − 8x + 7) ÷ (x − 1)

`"x"-1)overline("x"^3-8"x"+7)("x"^2-7"x"-7`

          x³ − x²
       −       +           
       − 7x² + 7
       − 7x² + 7x
       +       −            
       − 7x + 7 
       − 7x + 7    
       +      −            
            ×                 

∴ Other side = x² − 7x − 7