Question

The area of a rectangle is given by the expression 2x^3+5x^2-2x+3 . If the length of the rectangle is given by the expression x + 3, find the expression that represents the width

Answer 1

Answer:

2x^2 - x + 1

Step-by-step explanation:

This is polynomial long division:

Divide x + 3 into 2x^3 + 5X^2 - 2x + 3:

  Divide 2x^3 by x = 2x^2

  Multiple 2x^2 by (x + 3) =  2x^3 + 6x^2

  Subtract that from 2x^3 + 5X^2 - 2x + 3 = -x^2 -2x + 3

  Divide -x^2 by x = -x

  Multiple -x by (x + 3) = -x^2 - 3x

  Subtract that from -x^2 - 2x + 3 =  x + 3

  Divide x by x = 1

  Multiple 1 by (x + 3) = x + 3

  Subtract from x + 3 = 0