Exam 4 Review - Kent
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 4.6 - |Quadratic and Polynomial Inequalities |
| |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 [pic]
3. Use synthetic division to divide the following. Name the quotient and remainder
[pic] 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, [pic].
a) Use factoring to find values for x that make V=0.
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) [pic]
b) [pic]
7. Solve this quadratic inequality using both the graph method and the sign chart.
3x² + 5x – 2 ≤ 0
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