College Algebra 6/e   Barnett/Ziegler/Byleen
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Chapter 4: Polynomial and Rational Functions

Worked Exercises

Chapter 4: Polynomial and Rational Functions

Use synthetic division to write the quotient P(x) / (x - r) in the form P(x)/(x - r) = Q(x) + R/(x - r), where R is a constant.

Solution

Graph the polynomial function using synthetic division and the remainder theorem. Then describe the graph verbally, including the number of x intercepts, the number of turning points, and the left and right behaviour.

Solution

Solution

List all possible rational zeros for the given polynomial.

Solution

Find all roots exactly (rational, irrational, and imaginary) for the polynomial equation.

Solution

Find all zeros exactly (rational, irrational, and imaginary) for each polynomial.

Solution

Solve the inequality.

Solution

Find all other zeros of P(x), given the indicated zero.

Solution

Use a synthetic division table and Theorem 1 to locate each real zero between successive integers.

Solution

(A) Find the smallest possitive integer and largest negative integer that, by Theorem 2, are upper and lower bounds, respectively, for the real zeros of P(x). Also note the location of any zeros between successive integers.
(B) Approximate to one decimal place the largest real zero of P(x) using the bisection method.

Solution

(A) Find the smallest positive integer and larger negative integer that, by Theorem 2, are upper and lower bounds, respectively, for the real zeros of P(x).
(B) Approximate the real zeros of each polynomial to two decimal places.

Solution

APPLICATIONS

Solution

Solution

Find the domain and x intercepts. Do not graph.

Solution

Solution

Find all vertical and horizontal asymptotes. Do not graph.

Solution

Solution

Find all vertical, horizontal, and oblique asymptotes. Do not graph.

Solution

APPLICATION

Solution

Find constants A, B, C, and D, so that the right side is equal to the left.

Solution

Decompose into partial fractions.

Solution

Solution

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