Question 255055
The volume of a rectangle prism is represented by the expression 6x^3-7x^2-x-2 . the length is 2x-1 find expressions to represent the width and height of the prism
a) x and 3x-2 b) 3x-2 and x-1 c) x and 3x+2 d) 3x+2 and x+1

First off this should be 6x^3+7x^2-x-2.

2x-1 into 6x^3 - 7x^2 - x -2 --> 3x^2
 subtract 6x^3 - 3x^2
2x-1 into      - 4x^2 - x -2 --> -2x
 subtract      - 4x^2 +2x
2x-1 into             -3x -2 --> -3/2
 subtract             -3x + 3/2 
as you can see this leaves a remainder (well if they insist on original expression just choose none of the above cause none of the answers will neatly work)

2x-1 into 6x^3 + 7x^2 -x -2 --> 3x^2
 subtract 6x^3 - 3x^2
2x-1 into       10x^2 -x -2 --> 5x
 subtract       10x^2 -5x
2x-1 into             4x -2 --> 2

so what factors 3x^2+5x+2 ?
(3x+2)(x+1) = 3x^2+2x+3x+2 = 3x^2+5x+2

so answer is d