Question

The polynomial 2x2 + 900x represents the budget surplus of the town of Alphaville. Betaville's surplus is

represented by x2 -200x + 30,000. If x represents the tax revenue in thousands from both towns, enter
the expression that represents the total surplus of both towns together.

Answer 1

To determine the total budget surplus of Alphaville and Betaville together, add their respective surplus polynomials, yielding a combined expression of 3x^2 + 700x + 30,000.

Step-by-step explanation:

To find the expression that represents the total surplus of both towns together, we need to add together the polynomials for each town's surplus. The polynomial 2x2 + 900x represents the budget surplus of the town of Alphaville, and Betaville's surplus is represented by x2 -200x + 30,000. Adding these two expressions together, we get:

• 2x2 + 900x (Alphaville's surplus)
• + x2 - 200x + 30,000 (Betaville's surplus)

Combining like terms, we get:

3x2 + 700x + 30,000

This is the expression that represents the total surplus when x represents the tax revenue in thousands from both towns.