The area of a rectangle is represented by the polynomial 3x^2-7x-6. If the length of the rectangle is the factor (3x+2), then what is the factor of the width. (A=length x width)

Answer 1

A = LxW = 3x²-7x-6. From the quadratic formula, a=3, b=-7 and c=-6

Let L = 3x+2.

Since c = -6, it has to be the product of 2 (from L) and -3. -3 x 2 = -6

Since a = 3, it has to be the product of 3x (from L) and 1x. 3x * 1x = 3x²

Therefore W = x - 3

LxW = (3x+2) x (x-3) = 3x*x + 3x*-3 + 2*x + 2*-3 = 3x² - 9x + 2x - 6 = 3x² - 7x - 6