I need help on my homework with steps

Question

19. A wooden door contains a rectangular window. The width of the window is ( ) x − 2 feet. The area of the window can be represented by X^2-3X+2

a. Write a binomial that represents the height of the window.

b. The height of the door is 5 feet more than the height of the window. Write a polynomial that represents the height of the door.

c. The area of the door can be represented by 2 x + 4 . x The area is 32 square feet. Find the width and the height of the window.

Answer 1

a. height of the window is x-1

b. height of the door is x+4

c. It's unclear what" 2x+4.x" means. Assuming it means (2x+4)x as the area, then the window is

a little more than 1 x 2 feet. The door contains the window, so the window is smaller than the door.

the door is (x+4)(width)=32 with width of the door greater than width of the window = x-2

Area of window = x² - 3x +2 = (width)(height)

width of window is x-2 so height of window = (x²-3x+2)/(x-2)

x²-3x+2 = (x-2)(x-1) The x-2 factor cancels and the height of the window is x-1

height of the door is height of the window plus five = x-1+5 = x+4

Area of the door = 32 = (2x+4)x = 2x² + 4x

2x²+4x-32=0 or x²+2x-16=0

Use the quadratic formula, as this doesn't factor easily, but this is a factoring problem, so

I suspect the area of the door is a typo of some sort, as 2x+4.x is unclear

But using the quadratic formula gives x = (-2+(4+64)^1/2)/2 = -1+(17)^1/2 = a little over 3

You can ignore the negative square root as it gives a negative width or height.

width of window = x-2 or a little over 1

height of window = x-1 or a littler over 2

The window is a little over 2 x 1 feet

But "2x+4.x" doesn't make sense, and that's why the formula for the area for the door couldn't be factored if this is supposed to be a factoring problem. Or maybe someone else can understand what "2x+4.x" means.