ClassZone: Algebra II - Problem Solving Help

Problem Solving Help

6.3 Adding, Subtracting, and Multiplying Polynomials

Lesson 6.3: Help for Exercise 69 on page 343

A polynomial expression is given for the value of Mark's account on January 1, 2000. Notice that each term contains the binomial (1 + r) raised to a power of 1, 2, or 3. Furthermore, the coefficient of each term is equal to the amount of each deposit. The length of time each amount has been deposited is equal to the exponent on the binomial expression (1 + r). This means that an exponent of 3 on the binomial (1 + r) corresponds to the deposit made in 1997 (three years before January 1, 2000).

You can find an expression for the value of Tom's account by repeating this pattern with Tom's deposit amounts. The combined value of both accounts is equal to the sum of the two polynomials. In order to put this polynomial in standard form, multiply out each term using the special product patterns given on page 339, and then collect like terms.