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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