Polynomial Functions

Polynomial Functions 1) Use synthetic division to express P(x) = 3x3 – 2x2 – 6x – 4 in the form (divisor)(quotient) + remainder for the divisor x – 1

2) Use synthetic division to perform

x 3 − x 2 − 5x + 6 x−2

3) Use the remainder theorem to find the remainder that occurs when P(x) = -3x3 – x + 1 is divided by x + 2

4) Use the factor theorem to decide whether the statement is true. x + 1 is a factor of 3x5 + 4x2 – 7

5) If 1 is a zero of x3 + 6x2 + 5x – 12, what are the other zeros?

6) Find a polynomial with the given zeros 1, 0, and -1

7) Write a third degree polynomial with real coefficients and the given roots 1 and i

8) Use Descartes’ Rule of Signs to find the number of possible positive, negative, and non-real roots of 2x3 + 7x2 + 5x + 5 = 0

9) Find integer bounds for the roots of the equation 9x2 – 6x – 1 = 0

Practice 5.1 #11, 19, 21, 23, 27, 29, 39, 45, 51, 57, 63, 65, 69 5.2 #11, 15, 17, 21, 25, 37, 39