College algebra

Question

a rectangle patio has an area of x^3 + 12x^2+20x - 96. Find the length if the width is x-2. 

Answer 1

A=LW=x³+12x²+20x-96 with W=x-2

(note: you can check that x-2 is a factor of A by

plugging in 2 and getting 0)

Divide x³+12x²+20x-96 by x-2 to get L.

Synthetic division gives:

 

2 | 1   12    20   -96

   |        2    28    96

     1   14    48  |   0

 

So L=x²+14x+48 

(Note: the remainder is 0 as it should be; you can also check the answer by  multiplying the expressions for W and L to get A again.)