Last year, Mark designed a square-shaped banner for culture events at his school. This year, he is designing a similar banner for his school's sporting events. The sports banner is 12 inches longer than the length of the banner for the culture events. The area of the sporting events banner is given by the expression below, where x represents the side length, in inches, of the culture banner. Match each part of the expression with what it represents. the length of the sports banner the area of the culture banner the increase in area of the culture banner to make the sports banner the width of the sports banner the second degree term of the expression x2 + 12x arrowRight the first degree term of the expression x2 + 12x arrowRight the monomial, x, a factor of the expression x2 + 12x arrowRight the binomial, (x + 12), a factor of the expression x2 + 12x arrowRight

the second degree term of the expression x^2 + 12x arrowRight the area of the culture banner

the first degree term of the expression x^2 + 12x arrowRight the increase in area of the culture banner to make the sports banner

the monomial, x, a factor of the expression x^2 + 12x arrowRight the width of the sports banner

the binomial, (x + 12), a factor of the expression x^2 + 12x arrowRight the length of the sports banner

Explanation:

The problem statement tells you x is the side length of the culture banner, and also the side length of the sports banner. It also tells you the length of the sports banner is 12 (inches) more than that of the culture banner, a value that can be written as x+12.

Of course, the area of a rectangle is the product of its length and width dimensions. Since the culture banner is a square of side length x, its area will be x^2. Since the sports banner is 12 inches longer and still x inches wide, the increase in area that represents will be 12x.