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

See answers below.

Step-by-step 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

x^6

step-by-step explanation:

this is correct because:

x-6=0

0*x=0

so

x^6