If the rectangle is 2x^3 + 5x^2 -x -6 square centimeters. Write a polynomial that represents its width if its length is 2x^2 +x -3 cm.

Question

Please help me and kinda show the complete solution. Thank you in advance!

Answer 1

The rectangle's area (given) is length*width, so width=(2x^3+5x^2-x-6)/(2x^2+x-3). We can take a guess at the answer, x+2, because we need to multiply 2x^2 by x to get 2x^3 and we need to multiply -3 by 2 to get -6.

Multiply 2x^2+x-3 by x: 2x^3+x^2-3x, then multiply it by 2: 4x^2+2x-6. Add these results together and, bingo!, we get 2x^3+5x^2-x-6. So the width is in fact x+2. This is a first degree polynomial in x.