Subtracting Polynomials
You are enlarging a 5-inch by 7-inch photo by a scale factor of x and mounting it on a mat. You want the mat to be twice as wide as the enlarged photo and 2 inches less than twice as high as the enlarged photo.
a. Draw a diagram to represent the described situation. Label the dimensions.
b. Write a model for the area of the mat around the photograph as a function of the scale factor.
SOLUTION
Use a verbal model. Use the diagram to find expression for the labels.
Area of mat = Total Area - Area of photo
Area of mat = A (square inches)
Total area = (square inches)
Area of photo = (square inches)
Algebraic Model
A model for the area of the mat around the photograph as a function of the scale factor x is