UWorld SAT® Question of the Week
Interpret a polynomial expression in the context of area and volume

The formula for the area of a rectangle is A=lw, where l is the length and w is the width.  It is given that the length is 5 less than 2 times the width, so l = 2w – 5

The function notation A(w ) means the area in terms of the length w.  Substitute 2w – 5 for l into the expression for area to write an expression for A(w ).

Distribute w to each term in 2w − 5 to find the area of the field.

The area of the field, in square yards, is A(w ) = 2w ² − 5w.

(Choice A)  A(w ) = 3w − 5 may result from mistakenly adding (instead of multiplying) the length and the width of the field.

(Choice B)  A(w ) = 2w ² may result from mistaking the length to be 2 times the width, but it is given that the length is 5 less than 2 times the width.

(Choice D)  A(w ) = 3w ² may result from the misconception that “5 less than 2 times the width” can be represented by (5 − 2)w instead of 2w − 5.

Things to remember:
The formula for the area of a rectangle is A = lw where l  is the length and w  is the width.