The polynomial functionwill give the maximum number of interior regions formed in a circle if x points on the circumference are joined by all possible chords. For x = 1, 2, 3, 4, and 5, see FIGURES A–E.

For example, in FIGURE A we have 1 point, and because no chords can be drawn, we have only 1 interior region. In FIGURE B there are 2 points, and 2 interior regions are formed. Apply this information and work Exercises in order.

Observe a pattern in the results of Exercises 97–99. Use the pattern to make a logical prediction for the value of ƒ(6). Does the prediction equal ƒ(6)?

Data from in Exercise 97–99

Use the given polynomial function to verify that ƒ(1) = 1 and ƒ(2) = 2.

Based on the appropriate figure alone, what is a logical prediction for the value of

Verify the answers in Exercise 98 by evaluating ƒ(3), ƒ(4), and ƒ(5).

f(x) = = 1 -x4 24 - 1 23 x3 + -x 24 4 3 4 -x + 1