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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 (6x + 10) wide by (3x + 4) long. The dimensions of the spa are (5x + 2) wide by (2x + 1) long.


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

A8x2 + 63x + 42

B28x2 + 63x + 42

C28x2 + 45x + 38

D8x2 + 45x + 38

Verified Answer :

Brittxny

This is a polynomial minus polynomial problem. But first, we have to find the areas of the deck and the spa.

Deck:
(6x + 10)(3x + 4)
18x^2 + 24x + 30x + 40
18x^2 + 54x + 40

Spa:
(5x + 2)(2x + 1)
10x^2 + 5x + 4x + 2
10x^2 + 9x + 2

Deck area - Spa area
(18x^2 + 54x + 40) - (10x^2 + 9x + 2)

18x^2 - 10x^2= 8x^2
54x - 9x= 45x
40 - 2= 38
>>> 8x^2 + 45x + 38

In conclusion, the answer is (d) 8x^2 + 45x + 38.

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