Question

Write a polynomial to represent the larger rectangle and the smaller rectangle.

Answer 1

See answers below.

Explanation:

Large Rectangle: length x width = (x + 3)(x - 4) =

x² - 4x + 3x - 12

x² - x - 12

Smaller Rectangle: length x width = (x)(3) = 3x

Shaded Region: shaded area = lg. rectangle minus small rectangle

A = (x² - x - 12) - 3x

A = x² - 4x - 12

Solve for x, if shaded reion's area is 48 square units:

48 = x² - 4x - 12

x² - 4x - 12 -48 = 0

x² - 4x - 60 = 0

(x - 10)(x + 6) = 0

x - 10 = 0 or x + 6 = 0

x = 10 or x = -6

But x represents a length, so x cannot be -6.

x = 10