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

2x^2 - x + 1

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