Polynomial Review Problems

Review all the activities leading to Midterm 3. Review all the problems in the previous online homework sets (8+9+10).

MA109, Activity 34: Review (Sections 3.6+3.7+4.1+4.2+4.3) Date: Objective: Additional Assignments: To prepare for Midterm 3, make sure that you can solve the types of problems listed in Activities 33 and

Question 1: The graphs of y = p(x) are given in following figure, for some Polynomials p(x). Find the number of zeroes of p(x), in each case.

Class X - NCERT Maths EXERCISE NO:.1 Question 1: The graphs of y = p(x) are given in following figure, for some Polynomials p(x). Find the number of zeroes of p(x), in each case. (i) (ii) (iii) (iv) (v)

, a 1. , a 2. ,..., a n

CHAPTER Points to Remember :. Let x be a variable, n be a positive integer and a 0, a, a,..., a n be constants. Then n f ( x) a x a x... a x a, is called a polynomial in variable x. n n n 0 POLNOMIALS.

Chapter 3: Polynomial and Rational Functions

Chapter 3: Polynomial and Rational Functions 3.1 Polynomial Functions and Their Graphs A polynomial function of degree n is a function of the form P (x) = a n x n + a n 1 x n 1 + + a 1 x + a 0 The numbers

Downloaded from

Question 1: Exercise 2.1 The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x), in each case. (i) (ii) (iii) Page 1 of 24 (iv) (v) (v) Page

CHAPTER 2 POLYNOMIALS KEY POINTS

CHAPTER POLYNOMIALS KEY POINTS 1. Polynomials of degrees 1, and 3 are called linear, quadratic and cubic polynomials respectively.. A quadratic polynomial in x with real coefficient is of the form a x

(a) Write down the value of q and of r. (2) Write down the equation of the axis of symmetry. (1) (c) Find the value of p. (3) (Total 6 marks)

1. Let f(x) = p(x q)(x r). Part of the graph of f is shown below. The graph passes through the points ( 2, 0), (0, 4) and (4, 0). (a) Write down the value of q and of r. (b) Write down the equation of

2.6. Graphs of Rational Functions. Copyright 2011 Pearson, Inc.

2.6 Graphs of Rational Functions Copyright 2011 Pearson, Inc. Rational Functions What you ll learn about Transformations of the Reciprocal Function Limits and Asymptotes Analyzing Graphs of Rational Functions

Section 5.1 Determine if a function is a polynomial function. State the degree of a polynomial function.

Test Instructions Objectives Section 5.1 Section 5.1 Determine if a function is a polynomial function. State the degree of a polynomial function. Form a polynomial whose zeros and degree are given. Graph

Ch 7 Summary - POLYNOMIAL FUNCTIONS

Ch 7 Summary - POLYNOMIAL FUNCTIONS 1. An open-top box is to be made by cutting congruent squares of side length x from the corners of a 8.5- by 11-inch sheet of cardboard and bending up the sides. a)

Quadratics. SPTA Mathematics Higher Notes

H Quadratics SPTA Mathematics Higher Notes Quadratics are expressions with degree 2 and are of the form ax 2 + bx + c, where a 0. The Graph of a Quadratic is called a Parabola, and there are 2 types as

3 Polynomial and Rational Functions

3 Polynomial and Rational Functions 3.1 Polynomial Functions and their Graphs So far, we have learned how to graph polynomials of degree 0, 1, and. Degree 0 polynomial functions are things like f(x) =,

Math 1310 Section 4.1: Polynomial Functions and Their Graphs. A polynomial function is a function of the form ...

Math 1310 Section 4.1: Polynomial Functions and Their Graphs A polynomial function is a function of the form... where 0,,,, are real numbers and n is a whole number. The degree of the polynomial function

Chapter 2 Polynomial and Rational Functions

Chapter 2 Polynomial and Rational Functions Section 1 Section 2 Section 3 Section 4 Section 5 Section 6 Section 7 Quadratic Functions Polynomial Functions of Higher Degree Real Zeros of Polynomial Functions

Section Properties of Rational Expressions

88 Section. - Properties of Rational Expressions Recall that a rational number is any number that can be written as the ratio of two integers where the integer in the denominator cannot be. Rational Numbers:

1. Definition of a Polynomial

1. Definition of a Polynomial What is a polynomial? A polynomial P(x) is an algebraic expression of the form Degree P(x) = a n x n + a n 1 x n 1 + a n 2 x n 2 + + a 3 x 3 + a 2 x 2 + a 1 x + a 0 Leading

Table of contents. Polynomials Quadratic Functions Polynomials Graphs of Polynomials Polynomial Division Finding Roots of Polynomials

Table of contents Quadratic Functions Graphs of Polynomial Division Finding Roots of Jakayla Robbins & Beth Kelly (UK) Precalculus Notes Fall 2010 1 / 65 Concepts Quadratic Functions The Definition of

Lesson 9 Exploring Graphs of Quadratic Functions

Exploring Graphs of Quadratic Functions Graph the following system of linear inequalities: { y > 1 2 x 5 3x + 2y 14 a What are three points that are solutions to the system of inequalities? b Is the point

1) The line has a slope of ) The line passes through (2, 11) and. 6) r(x) = x + 4. From memory match each equation with its graph.

Review Test 2 Math 1314 Name Write an equation of the line satisfying the given conditions. Write the answer in standard form. 1) The line has a slope of - 2 7 and contains the point (3, 1). Use the point-slope

Polynomial Functions and Models

1 CA-Fall 2011-Jordan College Algebra, 4 th edition, Beecher/Penna/Bittinger, Pearson/Addison Wesley, 2012 Chapter 4: Polynomial Functions and Rational Functions Section 4.1 Polynomial Functions and Models

Chapter 2: Polynomial and Rational Functions

Chapter 2: Polynomial and Rational Functions Section 2.1 Quadratic Functions Date: Example 1: Sketching the Graph of a Quadratic Function a) Graph f(x) = 3 1 x 2 and g(x) = x 2 on the same coordinate plane.

6x 3 12x 2 7x 2 +16x 7x 2 +14x 2x 4

2.3 Real Zeros of Polynomial Functions Name: Pre-calculus. Date: Block: 1. Long Division of Polynomials. We have factored polynomials of degree 2 and some specific types of polynomials of degree 3 using

Math 2: Algebra 2, Geometry and Statistics Ms. Sheppard-Brick Chapter 4 Test Review

Chapter 4 Test Review Students will be able to (SWBAT): Write an explicit and a recursive function rule for a linear table of values. Write an explicit function rule for a quadratic table of values. Determine

Chapter REVIEW ANSWER KEY

TEXTBOOK HELP Pg. 313 Chapter 3.2-3.4 REVIEW ANSWER KEY 1. What qualifies a function as a polynomial? Powers = non-negative integers Polynomial functions of degree 2 or higher have graphs that are smooth

Chapter 2 notes from powerpoints

Chapter 2 notes from powerpoints Synthetic division and basic definitions Sections 1 and 2 Definition of a Polynomial Function: Let n be a nonnegative integer and let a n, a n-1,, a 2, a 1, a 0 be real

Functions and Equations

Canadian Mathematics Competition An activity of the Centre for Education in Mathematics and Computing, University of Waterloo, Waterloo, Ontario Euclid eworkshop # Functions and Equations c 006 CANADIAN

Chapter 2 Formulas and Definitions:

Chapter 2 Formulas and Definitions: (from 2.1) Definition of Polynomial Function: Let n be a nonnegative integer and let a n,a n 1,...,a 2,a 1,a 0 be real numbers with a n 0. The function given by f (x)

Core Mathematics 2 Algebra

Core Mathematics 2 Algebra Edited by: K V Kumaran Email: kvkumaran@gmail.com Core Mathematics 2 Algebra 1 Algebra and functions Simple algebraic division; use of the Factor Theorem and the Remainder Theorem.

The Graphs of Polynomial Functions

Section 4.3 The Graphs of Polynomial Functions Objective 1: Understanding the Definition of a Polynomial Function Definition Polynomial Function n n 1 n 2 The function f() x = anx + an 1x + an 2x + L +

Section 0.2 & 0.3 Worksheet. Types of Functions

MATH 1142 NAME Section 0.2 & 0.3 Worksheet Types of Functions Now that we have discussed what functions are and some of their characteristics, we will explore different types of functions. Section 0.2

REVIEW, pages Chapter 1: Polynomial Expressions and Functions Review Solutions DO NOT COPY. P 1.1. Write the division statement.

REVIEW, pages 72 77 1.1 1. Use long division to divide 7x 3 + 6x 4-7x - 9x 2 + 8 by x 1. Write the division statement. Write the polynomial in descending order: 6x 4 7x 3 9x 2 7x 8 6x 4 6x 3 6x 3 13x 2

Twitter: @Owen134866 www.mathsfreeresourcelibrary.com Prior Knowledge Check 1) Simplify: a) 3x 2 5x 5 b) 5x3 y 2 15x 7 2) Factorise: a) x 2 2x 24 b) 3x 2 17x + 20 15x 2 y 3 3) Use long division to calculate:

S56 (5.1) Polynomials.notebook August 25, 2016

Q1. Simplify Daily Practice 28.6.2016 Q2. Evaluate Today we will be learning about Polynomials. Q3. Write in completed square form x 2 + 4x + 7 Q4. State the equation of the line joining (0, 3) and (4,

171S4.3 Polynomial Division; The Remainder and Factor Theorems. October 26, Polynomial Division; The Remainder and Factor Theorems

MAT 171 Precalculus Algebra Dr. Claude Moore Cape Fear Community College CHAPTER 4: Polynomial and Rational Functions 4.1 Polynomial Functions and Models 4.2 Graphing Polynomial Functions 4.3 Polynomial

171S4.3 Polynomial Division; The Remainder and Factor Theorems. March 24, Polynomial Division; The Remainder and Factor Theorems

MAT 171 Precalculus Algebra Dr. Claude Moore Cape Fear Community College CHAPTER 4: Polynomial and Rational Functions 4.1 Polynomial Functions and Models 4.2 Graphing Polynomial Functions 4.3 Polynomial

10/22/16. 1 Math HL - Santowski SKILLS REVIEW. Lesson 15 Graphs of Rational Functions. Lesson Objectives. (A) Rational Functions

Lesson 15 Graphs of Rational Functions SKILLS REVIEW! Use function composition to prove that the following two funtions are inverses of each other. 2x 3 f(x) = g(x) = 5 2 x 1 1 2 Lesson Objectives! The

Polynomial functions right- and left-hand behavior (end behavior):

Lesson 2.2 Polynomial Functions For each function: a.) Graph the function on your calculator Find an appropriate window. Draw a sketch of the graph on your paper and indicate your window. b.) Identify

Math 110 Midterm 1 Study Guide October 14, 2013

Name: For more practice exercises, do the study set problems in sections: 3.4 3.7, 4.1, and 4.2. 1. Find the domain of f, and express the solution in interval notation. (a) f(x) = x 6 D = (, ) or D = R

Algebra II: Strand 5. Power, Polynomial, and Rational Functions; Topic 3. Rational Functions; Task 5.3.1

TASK 5.3.: RATIONAL FUNCTIONS AND THEIR RECIPROCALS Solutions Rational functions appear frequently in business, science, engineering, and medical applications. This activity explores some aspects of rational

MAT116 Final Review Session Chapter 3: Polynomial and Rational Functions

MAT116 Final Review Session Chapter 3: Polynomial and Rational Functions Quadratic Function A quadratic function is defined by a quadratic or second-degree polynomial. Standard Form f x = ax 2 + bx + c,

Section 4.1: Polynomial Functions and Models

Section 4.1: Polynomial Functions and Models Learning Objectives: 1. Identify Polynomial Functions and Their Degree 2. Graph Polynomial Functions Using Transformations 3. Identify the Real Zeros of a Polynomial

King Fahd University of Petroleum and Minerals Prep-Year Math Program Math Term 161 Recitation (R1, R2)

Math 001 - Term 161 Recitation (R1, R) Question 1: How many rational and irrational numbers are possible between 0 and 1? (a) 1 (b) Finite (c) 0 (d) Infinite (e) Question : A will contain how many elements

PreCalculus: Semester 1 Final Exam Review

Name: Class: Date: ID: A PreCalculus: Semester 1 Final Exam Review Short Answer 1. Determine whether the relation represents a function. If it is a function, state the domain and range. 9. Find the domain

More Polynomial Equations Section 6.4

MATH 11009: More Polynomial Equations Section 6.4 Dividend: The number or expression you are dividing into. Divisor: The number or expression you are dividing by. Synthetic division: Synthetic division

Advanced Math Quiz Review Name: Dec Use Synthetic Division to divide the first polynomial by the second polynomial.

Advanced Math Quiz 3.1-3.2 Review Name: Dec. 2014 Use Synthetic Division to divide the first polynomial by the second polynomial. 1. 5x 3 + 6x 2 8 x + 1, x 5 1. Quotient: 2. x 5 10x 3 + 5 x 1, x + 4 2.

Student: Date: Instructor: kumnit nong Course: MATH 105 by Nong https://xlitemprodpearsoncmgcom/api/v1/print/math Assignment: CH test review 1 Find the transformation form of the quadratic function graphed

A repeated root is a root that occurs more than once in a polynomial function.

Unit 2A, Lesson 3.3 Finding Zeros Synthetic division, along with your knowledge of end behavior and turning points, can be used to identify the x-intercepts of a polynomial function. This information allows

2 the maximum/minimum value is ( ).

Math 60 Ch3 practice Test The graph of f(x) = 3(x 5) + 3 is with its vertex at ( maximum/minimum value is ( ). ) and the The graph of a quadratic function f(x) = x + x 1 is with its vertex at ( the maximum/minimum

Horizontal and Vertical Asymptotes from section 2.6

Horizontal and Vertical Asymptotes from section 2.6 Definition: In either of the cases f(x) = L or f(x) = L we say that the x x horizontal line y = L is a horizontal asymptote of the function f. Note:

Cumulative Review. Name. 13) 2x = -4 13) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Cumulative Review Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Evaluate the algebraic expression for the given value or values of the variable(s).

SB CH 2 answers.notebook. November 05, Warm Up. Oct 8 10:36 AM. Oct 5 2:22 PM. Oct 8 9:22 AM. Oct 8 9:19 AM. Oct 8 9:26 AM.

Warm Up Oct 8 10:36 AM Oct 5 2:22 PM Linear Function Qualities Oct 8 9:22 AM Oct 8 9:19 AM Quadratic Function Qualities Oct 8 9:26 AM Oct 8 9:25 AM 1 Oct 8 9:28 AM Oct 8 9:25 AM Given vertex (-1,4) and

Unit 1 Vocabulary. A function that contains 1 or more or terms. The variables may be to any non-negative power.

MODULE 1 1 Polynomial A function that contains 1 or more or terms. The variables may be to any non-negative power. 1 Modeling Mathematical modeling is the process of using, and to represent real world

Midterm Review. Name: Class: Date: ID: A. Short Answer. 1. For each graph, write the equation of a radical function of the form y = a b(x h) + k.

Name: Class: Date: ID: A Midterm Review Short Answer 1. For each graph, write the equation of a radical function of the form y = a b(x h) + k. a) b) c) 2. Determine the domain and range of each function.

Unit 4: Polynomial and Rational Functions

50 Unit 4: Polynomial and Rational Functions Polynomial Functions A polynomial function y px ( ) is a function of the form p( x) ax + a x + a x +... + ax + ax+ a n n 1 n n n 1 n 1 0 where an, an 1,...,

Section 4.3. Polynomial Division; The Remainder Theorem and the Factor Theorem

Section 4.3 Polynomial Division; The Remainder Theorem and the Factor Theorem Polynomial Long Division Let s compute 823 5 : Example of Long Division of Numbers Example of Long Division of Numbers Let

Chapter 2 Prerequisite Skills BLM Evaluate Functions 1. Given P(x) = x 4 3x 2 + 5x 11, evaluate.

Chapter Prerequisite Skills BLM 1.. Evaluate Functions 1. Given P(x) = x 4 x + 5x 11, evaluate. a) P( ) b) P() c) P( 1) 1 d) P 4 Simplify Expressions. Expand and simplify. a) (x x x + 4)(x 1) + b) (x +

Polynomial expression

1 Polynomial expression Polynomial expression A expression S(x) in one variable x is an algebraic expression in x term as Where an,an-1,,a,a0 are constant and real numbers and an is not equal to zero Some

Aim: How do we prepare for AP Problems on limits, continuity and differentiability? f (x)

Name AP Calculus Date Supplemental Review 1 Aim: How do we prepare for AP Problems on limits, continuity and differentiability? Do Now: Use the graph of f(x) to evaluate each of the following: 1. lim x

Exp, Log, Poly Functions Quarter 3 Review Name

Exp, Log, Poly Functions Quarter 3 Review Name Textbook problems for practice: p. 285-293; p. 293 #9-14, p. 294-5 #1-34, 49-52, 55,56, 57; p. 297-321 logs; p. 280-1 #11-84 *Blood Alcohol, Bungee-from binder

The final is cumulative, but with more emphasis on chapters 3 and 4. There will be two parts.

Math 141 Review for Final The final is cumulative, but with more emphasis on chapters 3 and 4. There will be two parts. Part 1 (no calculator) graphing (polynomial, rational, linear, exponential, and logarithmic

Lesson 7.1 Polynomial Degree and Finite Differences

Lesson 7.1 Polynomial Degree and Finite Differences 1. Identify the degree of each polynomial. a. 3x 4 2x 3 3x 2 x 7 b. x 1 c. 0.2x 1.x 2 3.2x 3 d. 20 16x 2 20x e. x x 2 x 3 x 4 x f. x 2 6x 2x 6 3x 4 8

Math 115 Spring 11 Written Homework 10 Solutions

Math 5 Spring Written Homework 0 Solutions. For following its, state what indeterminate form the its are in and evaluate the its. (a) 3x 4x 4 x x 8 Solution: This is in indeterminate form 0. Algebraically,

Reading Mathematical Expressions & Arithmetic Operations Expression Reads Note

Math 001 - Term 171 Reading Mathematical Expressions & Arithmetic Operations Expression Reads Note x A x belongs to A,x is in A Between an element and a set. A B A is a subset of B Between two sets. φ

Power and Polynomial Functions. College Algebra

Power and Polynomial Functions College Algebra Power Function A power function is a function that can be represented in the form f x = kx % where k and p are real numbers, and k is known as the coefficient.

Introduction. A rational function is a quotient of polynomial functions. It can be written in the form

RATIONAL FUNCTIONS Introduction A rational function is a quotient of polynomial functions. It can be written in the form where N(x) and D(x) are polynomials and D(x) is not the zero polynomial. 2 In general,

Unit 1: Polynomial Functions SuggestedTime:14 hours

Unit 1: Polynomial Functions SuggestedTime:14 hours (Chapter 3 of the text) Prerequisite Skills Do the following: #1,3,4,5, 6a)c)d)f), 7a)b)c),8a)b), 9 Polynomial Functions A polynomial function is an

Section 3.2 Polynomial Functions and Their Graphs

Section 3.2 Polynomial Functions and Their Graphs EXAMPLES: P (x) = 3, Q(x) = 4x 7, R(x) = x 2 + x, S(x) = 2x 3 6x 2 10 QUESTION: Which of the following are polynomial functions? (a) f(x) = x 3 + 2x +

RF2 Unit Test # 2 Review Quadratics (Chapter 6) 1. What is the degree of a quadratic function?

RF Unit Test # Review Quadratics (Chapter 6) 1. What is the degree of a quadratic function? Name: a. 1 b. c. 3 d. 0. What is the -intercept for = 3x + x 5? a. 5 b. 5 c. d. 3 3. Which set of data is correct

College Algebra Notes

Metropolitan Community College Contents Introduction 2 Unit 1 3 Rational Expressions........................................... 3 Quadratic Equations........................................... 9 Polynomial,

March Algebra 2 Question 1. March Algebra 2 Question 1

March Algebra 2 Question 1 If the statement is always true for the domain, assign that part a 3. If it is sometimes true, assign it a 2. If it is never true, assign it a 1. Your answer for this question

Mathematical Olympiad Training Polynomials

Mathematical Olympiad Training Polynomials Definition A polynomial over a ring R(Z, Q, R, C) in x is an expression of the form p(x) = a n x n + a n 1 x n 1 + + a 1 x + a 0, a i R, for 0 i n. If a n 0,

Chapter 3 Polynomial Functions

Trig / Coll. Alg. Name: Chapter 3 Polynomial Functions 3.1 Quadratic Functions (not on this test) For each parabola, give the vertex, intercepts (x- and y-), axis of symmetry, and sketch the graph. 1.

Higher Portfolio Quadratics and Polynomials

Higher Portfolio Quadratics and Polynomials Higher 5. Quadratics and Polynomials Section A - Revision Section This section will help you revise previous learning which is required in this topic R1 I have

1. Which one of the following points is a singular point of. f(x) = (x 1) 2/3? f(x) = 3x 3 4x 2 5x + 6? (C)

Math 1120 Calculus Test 3 November 4, 1 Name In the first 10 problems, each part counts 5 points (total 50 points) and the final three problems count 20 points each Multiple choice section Circle the correct

QUADRATIC FUNCTIONS AND MODELS

QUADRATIC FUNCTIONS AND MODELS What You Should Learn Analyze graphs of quadratic functions. Write quadratic functions in standard form and use the results to sketch graphs of functions. Find minimum and

Pre-Algebra 2. Unit 9. Polynomials Name Period

Pre-Algebra Unit 9 Polynomials Name Period 9.1A Add, Subtract, and Multiplying Polynomials (non-complex) Explain Add the following polynomials: 1) ( ) ( ) ) ( ) ( ) Subtract the following polynomials:

Chapter 8. Exploring Polynomial Functions. Jennifer Huss

Chapter 8 Exploring Polynomial Functions Jennifer Huss 8-1 Polynomial Functions The degree of a polynomial is determined by the greatest exponent when there is only one variable (x) in the polynomial Polynomial

Tenth Maths Polynomials

Tenth Maths Polynomials Polynomials are algebraic expressions constructed using constants and variables. Coefficients operate on variables, which can be raised to various powers of non-negative integer

Georgia Department of Education Common Core Georgia Performance Standards Framework CCGPS Advanced Algebra Unit 2

Polynomials Patterns Task 1. To get an idea of what polynomial functions look like, we can graph the first through fifth degree polynomials with leading coefficients of 1. For each polynomial function,

Unit 2 Rational Functionals Exercises MHF 4UI Page 1

Unit 2 Rational Functionals Exercises MHF 4UI Page Exercises 2.: Division of Polynomials. Divide, assuming the divisor is not equal to zero. a) x 3 + 2x 2 7x + 4 ) x + ) b) 3x 4 4x 2 2x + 3 ) x 4) 7. *)

Chapter 2 Polynomial and Rational Functions

Chapter 2 Polynomial and Rational Functions Overview: 2.2 Polynomial Functions of Higher Degree 2.3 Real Zeros of Polynomial Functions 2.4 Complex Numbers 2.5 The Fundamental Theorem of Algebra 2.6 Rational

3.5. Dividing Polynomials. LEARN ABOUT the Math. Selecting a strategy to divide a polynomial by a binomial

3.5 Dividing Polynomials GOAL Use a variety of strategies to determine the quotient when one polynomial is divided by another polynomial. LEARN ABOU the Math Recall that long division can be used to determine

Chapter Five Notes N P U2C5

Chapter Five Notes N P UC5 Name Period Section 5.: Linear and Quadratic Functions with Modeling In every math class you have had since algebra you have worked with equations. Most of those equations have

Rational Functions. Elementary Functions. Algebra with mixed fractions. Algebra with mixed fractions

Rational Functions A rational function f (x) is a function which is the ratio of two polynomials, that is, Part 2, Polynomials Lecture 26a, Rational Functions f (x) = where and are polynomials Dr Ken W

Polynomial Expressions and Functions

Hartfield College Algebra (Version 2017a - Thomas Hartfield) Unit FOUR Page - 1 - of 36 Topic 32: Polynomial Expressions and Functions Recall the definitions of polynomials and terms. Definition: A polynomial

Core Mathematics 1 Quadratics

Regent College Maths Department Core Mathematics 1 Quadratics Quadratics September 011 C1 Note Quadratic functions and their graphs. The graph of y ax bx c. (i) a 0 (ii) a 0 The turning point can be determined

Skills Practice Skills Practice for Lesson 10.1

Skills Practice Skills Practice for Lesson.1 Name Date Higher Order Polynomials and Factoring Roots of Polynomial Equations Problem Set Solve each polynomial equation using factoring. Then check your solution(s).

Final Exam A Name. 20 i C) Solve the equation by factoring. 4) x2 = x + 30 A) {-5, 6} B) {5, 6} C) {1, 30} D) {-5, -6} -9 ± i 3 14

Final Exam A Name First, write the value(s) that make the denominator(s) zero. Then solve the equation. 1 1) x + 3 + 5 x - 3 = 30 (x + 3)(x - 3) 1) A) x -3, 3; B) x -3, 3; {4} C) No restrictions; {3} D)

Synthetic Substitution

Write your questions and thoughts here! 7.2 Synthetic and Long Polynomial Division 1 Use direct substitution to evaluate t a = a! a! + a + 5 when a = - 2 Synthetic Substitution Synthetic substitution is

MATH 121: EXTRA PRACTICE FOR TEST 2. Disclaimer: Any material covered in class and/or assigned for homework is a fair game for the exam.

MATH 121: EXTRA PRACTICE FOR TEST 2 Disclaimer: Any material covered in class and/or assigned for homework is a fair game for the exam. 1 Linear Functions 1. Consider the functions f(x) = 3x + 5 and g(x)

NAME DATE PERIOD. Power and Radical Functions. New Vocabulary Fill in the blank with the correct term. positive integer.

2-1 Power and Radical Functions What You ll Learn Scan Lesson 2-1. Predict two things that you expect to learn based on the headings and Key Concept box. 1. 2. Lesson 2-1 Active Vocabulary extraneous solution

b) since the remainder is 0 I need to factor the numerator. Synthetic division tells me this is true

Section 5.2 solutions #1-10: a) Perform the division using synthetic division. b) if the remainder is 0 use the result to completely factor the dividend (this is the numerator or the polynomial to the

Chapter 7 Polynomial Functions. Factoring Review. We will talk about 3 Types: ALWAYS FACTOR OUT FIRST! Ex 2: Factor x x + 64

Chapter 7 Polynomial Functions Factoring Review We will talk about 3 Types: 1. 2. 3. ALWAYS FACTOR OUT FIRST! Ex 1: Factor x 2 + 5x + 6 Ex 2: Factor x 2 + 16x + 64 Ex 3: Factor 4x 2 + 6x 18 Ex 4: Factor

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Calculus I - Homework Chapter 2 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the graph is the graph of a function. 1) 1)

Logarithms Dr. Laura J. Pyzdrowski

1 Names: (8 communication points) About this Laboratory An exponential function of the form f(x) = a x, where a is a positive real number not equal to 1, is an example of a one-to-one function. This means

Unit 3: HW3.5 Sum and Product

Unit 3: HW3.5 Sum and Product Without solving, find the sum and product of the roots of each equation. 1. x 2 8x + 7 = 0 2. 2x + 5 = x 2 3. -7x + 4 = -3x 2 4. -10x 2 = 5x - 2 5. 5x 2 2x 3 4 6. 1 3 x2 3x

Solve the problem. Determine the center and radius of the circle. Use the given information about a circle to find its equation.

Math1314-TestReview2-Spring2016 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) Is the point (-5, -3) on the circle defined

A field F is a set of numbers that includes the two numbers 0 and 1 and satisfies the properties:

Byte multiplication 1 Field arithmetic A field F is a set of numbers that includes the two numbers 0 and 1 and satisfies the properties: F is an abelian group under addition, meaning - F is closed under

Chapter 7 Algebra 2 Honors 1 Polynomials

Chapter 7 Algebra 2 Honors 1 Polynomials Polynomial: - - Polynomials in one variable Degree Leading coefficient f(x) = 3x 3 2x + 4 f(2) = f(t) = f(y -1) = 3f(x) = Using your graphing calculator sketch/graph

Power Functions and Polynomial Functions

CHAPTER Power Functions and Polynomial Functions Estuaries form when rivers and streams meet the sea, resulting in a mix of salt and fresh water. On the coast of Georgia, large estuaries have formed where