Exam 4 Review
Sections 4.0, 4.1, 4.2, 4.3, 4.4, 2.8, 4.6
Important Topics to Know:
Sec 4.0 Factoring polynomials, operations on higher degree polynomials; simplify, multiply,
divide, add/subtract rational expressions;
p. 376 # 4, 7, 8, 13, 16, 19, 22, 23, 25, 28
Sec 4.1 Cubic and Quartic functions, State end behavior, graph using calculator, evaluate and
interpret function values.
pp. 384 #5, 7, 8, 9, 11, 12, 25, 29, 41, 42
Sec 4.2 Cubic and Quartic Models, 3rd and 4th differences; use calculator to find regression
equation; pp. 394 # 1-4, 9, 17, 20, 23, 29, 30, 32
Sec 4.3 Solving polynomials by factoring, grouping and root method, Finding zeros
pp.407 # 1, 4, 5, 7, 9, 12, 22, 23, 25, 28, 29, 31, 33
Sec 4.4 Division of Polys, Synthetic division, Rational Zero Test, Finding solutions
pp. 418 #1, 2, 5, 8, 9, 12, 15, 19, 21, 23,25, 32, 34, 35
Sec 2.8 and
Quadratic and Polynomial Inequalities
4.6 p. 260: #19, 23, 25,
pp. 435 # 1, 5, 6, 11, 15, 19, 21, 22, 23, 25
Sec. 4.5
Be able to find domain of rational functions and their vertical asymptotes.
HANDBOOK End behavior: p. 175; Division: p. 187-88; Rational zeros: p. 189-190; inequalities: p.
195
Look at the chapter summary problems beginning on p.440 for additional practice.
**Also use quizzes to help you study!!!
Things to know:
 Recognize the differences and similarities between polynomial functions, noting end behavior on
both left and right hand sides, x-intercepts, y-intercepts, turning points, effects of leading
coefficient.

Simplifying polynomial expressions by factoring and canceling, long division and synthetic division.

Have the ability to identify the divisor, dividend, quotient and remainder.

If (x-c) is a factor of a function then c is a zero of that function. If (x+c) is a factor of a
function then -c is a zero of that function.

If c is a zero of a function then (x-c) is a factor of that function. If -c is a zero is a factor
of a function then (x+c) is a factor of that function

Possible zeros of a function are found using the Rational Zeros Test. The numerators are factors
of the constant term and the denominators are factors of the leading coefficient.

Use synthetic division to test the zeros of a polynomial function. Once reduced to a quadratic
function (degree 2) it can be factored or use quadratic formula to solve.


Use a sign chart to find the solutions of a quadratic or cubic polynomial inequality.
Simplify, multiply, or add/subtract rational expressions; Find domain and vertical asymptotes of
rational function
Try some of these:
1. Describe the end behavior of f(x) = -5x6 on both the left and right hand side.
LHS:
RHS:
2. Solve 0  x  16 x
3
3. Use synthetic division to divide the following. Name the quotient and remainder
x 4  4 x 2  16
x2
quotient:
remainder:
4. Find a polynomial of degree 4 that has the following zeros: -2, 0, 2, and 4.
5. The volume of a box that can be formed by cutting out the corners of an 18 inch square
sheet of paper, is given by the function, V  324 x  72 x  4 x .
a) Use factoring to find values for x that make V=0.
2
3
x
x
18 inches
x
x
18 inches
b) What values for x are reasonable to actually make a box with positive volume? (Think
inequalities)
6. Find all the real zeros of each of the following. Be sure to show all steps, including
listing the possible rational zeros.
a)
P( x)  2 x 4  7 x3  12 x 2  3x  2
b)
P( x)  x 3  4 x 2  3x  2
7. Solve this quadratic inequality using both the graph method and the sign chart.
3x² + 5x – 2 ≤ 0