Seth, a carpenter, is helping a client remodel her backyard patio entryway. The entryway will have a set of double doors that are trimmed with moulding. The double doors will be square, and the moulding will be $2$ inches wide along the top and sides of the door. The total area of the double doors and moulding in square inches can be modeled by the expression $(x + 4)(x + 2)$ , where $x$ is the width of the double doors in inches. This expression can also be written in the form $x^2 + 6x + 8$ . What does the quantity $6x + 8$ represent in the expression? $\newline$ (A)the area of the moulding in square inches $\newline$ (B)the height of the double doors and moulding together in inches $\newline$ (C)the perimeter around the outside of the double doors and moulding in inches $\newline$ (D)the area of the double doors in square inches

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Interpret parts of quadratic expressions: word problems

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Q. Seth, a carpenter, is helping a client remodel her backyard patio entryway. The entryway will have a set of double doors that are trimmed with moulding. The double doors will be square, and the moulding will be

2

inches wide along the top and sides of the door. The total area of the double doors and moulding in square inches can be modeled by the expression

(x + 4)(x + 2)

, where

x

is the width of the double doors in inches. This expression can also be written in the form

x^2 + 6x + 8

. What does the quantity

6x + 8

represent in the expression?

\newline

(A)the area of the moulding in square inches

\newline

(B)the height of the double doors and moulding together in inches

\newline

(C)the perimeter around the outside of the double doors and moulding in inches

\newline

(D)the area of the double doors in square inches

Total Area Expression: The expression for the total area is $(x + 4)(x + 2)$ , which expands to $x^2 + 6x + 8$ .
Square Double Doors: The $x^2$ term represents the area of the square double doors, since area of a square is side length squared.
Moulding Area Calculation: The $6x$ term comes from adding the areas of the moulding on the sides and top, which are $2x$ (top), $2x$ (left side), and $2x$ (right side), adding up to $6x$ .
Corner Moulding Area: The $+8$ term represents the area of the moulding at the corners, since there are four corners and each corner is a $2$ -inch by $2$ -inch square, so $4 \times 2 \times 2 = 16$ , but this is incorrect, it should be $4 \times 2 = 8$ .