Question

The area, A, of a rectangle is 120x2 + 78x – 90, and the length, l, of the rectangle is 12x + 15. Which of the following gives the width, w, of the rectangle?

9x + 4

10x – 19

10x – 6

8x – 6

Answer 1

for a rectangle:

area = length*width

therefore width = area/length

so you'll need to divide the area polynomial (120x^2 + 78x – 90) by the length polynomial (12x + 15). to make the arithmetic easier, factor out 3 from both expressions, then since you're dividing them, the 3 will cancel out during the division process (so cancel out the 3 you factored out)

from there, set up the polynomial long division

Answer 2

alternative method: you could try factoring the area polynomial to see if you can get the length as one of the two factors. the other factor will be the width polynomial.