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A carpenter is assigned a job of installing a spa into a pre-existing deck. The dimensions of the deck are (5x + 2) wide by (3x + 1) long. The dimensions of the spa are (2x + 3) wide by (x + 2) long.

Write the polynomial that represents the remaining area of the deck after the carpenter cut the hole out for the spa.

(A) 17x2 + 18x + 8

(B) 13x2 + 18x + 8

(C) 13x2 + 4x - 4

(D) 17x2 + 4x - 4

Respuesta :

camdenarringto
I drew two rectangles; one representing the deck and one representing the spa. Now label the sides like the problem stated. 

The question asks for the area LEFT OVER, meaning the difference (subtract). 
the polynomial you get is:
(5x+2)(3x+1)-(2x+3(x+2))
In order to simplify, use the FOIL method. That gives you
15x²+5x+6x+2-(2x²+4x+3x+6)
Next, distribute the negative to all the terms within the parentheses. 
That yields 13x²+4x-4

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