Register now to access 7 million high quality study materials (What's Course Hero?) Course Hero is the premier provider of high quality online educational resources. With millions of study documents, online tutors, digital flashcards and free courseware, Course Hero is helping students learn more efficiently and effectively. Whether you're interested in exploring new subjects or mastering key topics for your next exam, Course Hero has the tools you need to achieve your goals.
4 Pages
1300_notes_3_2_done
Course: M 1300, Fall 2009School: U. Houston
Rating:
Word Count: 589
Document Preview
1300 Math Operations with Polynomials Section 3.2 Notes Addition of Polynomials The sum of two polynomials is found by combining like terms. To add like terms, add the coefficients and do not change the variable and exponents in common. Example: Perform the addition (2x7 + 9x3 - 5) + (3x3 + 2x + 14). (2x7 + 9x3 - 5) + (3x3 + 2x + 14) Remove the parentheses and group like terms together 7 3 3 2x + 9x + 3x + 2x +...
Unformatted Document Excerpt
Coursehero >> Texas >> U. Houston >> M 1300Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
1300 Math Operations with Polynomials
Section 3.2 Notes
Addition of Polynomials The sum of two polynomials is found by combining like terms. To add like terms, add the coefficients and do not change the variable and exponents in common. Example: Perform the addition (2x7 + 9x3 - 5) + (3x3 + 2x + 14). (2x7 + 9x3 - 5) + (3x3 + 2x + 14) Remove the parentheses and group like terms together 7 3 3 2x + 9x + 3x + 2x + 14 - 5 Combine like terms. Don't change variables or exponents. 2x7 + 12x3 + 2x + 9 Answer. Example: Perform the addition (2x3 - 17x2 - 5x) + (3x3 - x + 8). (2x3 - 17x2 - 5x) + (3x3 - x + 8) Remove the parentheses and group like terms together 2x3 + 3x3 - 17x2 - 5x - x + 8 Combine like terms. Don't change variables or exponents. 3 2 5x - 17x - 6x + 8 Answer. Subtraction of Polynomials The difference of two polynomials is found by adding the first polynomial to the negative of the second polynomial. The negative of the second polynomial is found by changing the sign of each term of the polynomial. Example: Perform the subtraction (9x5 + 2x3 - 1) - (2x3 + 4x - 4). Create the negative of the second polynomial. (9x5 + 2x3 - 1) - (2x3 + 4x - 4) 5 3 3 (9x + 2x - 1) + (-2x - 4x + 4) Add, removing the parentheses and grouping like terms. 9x5 + 2x3 - 2x3 - 4x - 1 + 4 Combine like terms. 9x5 - 4x + 3 Answer. Example: Perform the subtraction (5x2 - 7x + 2) - (x2 + 4x - 3). (5x2 - 7x + 2) - (x2 + 4x - 3) Create the negative of the second polynomial. (5x2 - 7x + 2) + (-x2 - 4x + 3) Add, removing the parentheses and grouping like terms. 2 2 5x - x - 7x - 4x + 2 + 3 Combine like terms. 4x2 - 11x + 5 Answer. Multiplication of Polynomials Multiplication of polynomials is done by repeated use of the distributed property. Multiplication of binomials (two-termed polynomials) is done using the FOIL method. FOIL is an acronym which stands "first for terms, outside terms, inside terms, last terms." Example: Perform the multiplication (-7x + 2) (4x - 3). (-7x + 2) (4x - 3) Multiply the first, outside, inside and last terms and add. (-7x)(4x) + (-7x)(-3) + 2(4x) + 2(-3) Simplify. Combine like terms. -28x2 + 21x + 8x - 6 -28x2 + 29x - 6 Answer. Example: Perform the multiplication (9x3 - 5) (3x3 + 2x). (9x3 - 5) (3x3 + 2x) Multiply the first, outside, inside and last terms and add.
1
Math 1300
Section 3.2 Notes
(9x3)(3x3) + (9x3)(2x) + (-5)(3x3) + (-5)(2x) Simplify. 6 4 3 27x + 18x - 15x - 10x Answer. There are no like terms to combine. Example: Perform the multiplication (2x3 + 9x2 - 5)(3x2 + 2x + 14).
Distribute each term in the first group with each term in the second and add the results together. (2x3)(3x2) + (2x3)(2x) + (2x3)(14) + (9x2)(3x2) + (9x2)(2x) + (9x2)(14) + (-5)(3x2) + (-5)(2x) + (-5)(14) Multiply. Group like terms together. 6x5 + 4x4 + 28x3 + 27x4 + 18x3 + 126x2 - 15x2 - 10x - 70 5 4 4 3 3 2 2 6x + 4x + 27x + 28x + 18x + 126x - 15x - 10x - 70 Combine like terms. 6x5 + 31x4 + 46x3 + 111x2 - 10x - 70 Answ...
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more.
Course Hero has millions of course specific materials providing students with the best way to expand
their education.
Below is a small sample set of documents:
Below is a small sample set of documents:
U. Houston - M - 1300
Math 1300 Section 2.2 Note: For the final result, use a reduced radical form (i.e., write 8 as 2 2 ).Test 2 ReviewUse the Pythagorean Theorem to find the missing side of each of the following right triangles.1. 2. 3.If a = 5, c =7, find b. If
U. Houston - M - 1300
Section 2.2 1. b = 24 = 2 6 2. c = 125 = 5 5 3. a = 57 5 241 1 = 241 5. d = 100 10 17 6. d = 5 5 7. d = 8 641 1 8. d = = 641 100 10 9. d = 109 3 10. ,4 10 1 5 11. , 5 4 1 1 12. , 2 5 4. d =Section 2.3 13. m = undefined15 2 32 15. m
U. Houston - MATH - 3303
Sep 7-3:21 PM1Sep 7-4:05 PM2Sep 7-4:07 PM3Sep 7-4:12 PM4Sep 7-4:14 PM5Sep 7-4:15 PM6Sep 7-4:21 PM7Sep 7-4:24 PM8Sep 7-4:26 PM9Sep 7-4:27 PM10Sep 7-4:30 PM11Sep 7-4:33 PM12Sep 7-4:36 PM13Sep 7-4:44 P
U. Houston - MATH - 3303
Nov 16-3:55 PM1Nov 16-4:07 PM2Nov 16-4:08 PM3Nov 16-4:10 PM4Nov 16-4:14 PM5Nov 16-4:18 PM6Nov 16-4:24 PM7Nov 16-4:27 PM8Nov 16-4:29 PM9Nov 16-4:33 PM10Nov 16-4:35 PM11Nov 16-4:39 PM12Nov 16-4:42 PM13
U. Houston - MATH - 3303
Some good websites for continued fractions.http:/archives.math.utk.edu/articles/atuyl/confrac/intro.html http:/home.att.net/~srschmitt/script_fractions.html http:/perl.plover.com/yak/cftalk/
U. Houston - MATH - 3303
Homework Module 3 3303 Name: email address: phone number:Who helped me:Who I helped:Homework rules: Front side only. Keep the questions and your answers in order. If you send it pdf, send it in a single scanned file. (dog@uh.edu) If you turn
U. Houston - MATH - 3303
Oct 5-3:53 PM1Oct 5-3:58 PM2Oct 5-4:01 PM3Oct 5-4:07 PM4Oct 5-4:10 PM5Oct 5-4:14 PM6Oct 5-4:16 PM7Oct 5-4:18 PM8Oct 5-4:21 PM9Oct 5-4:23 PM10Oct 5-4:26 PM11Oct 5-4:30 PM12Oct 5-4:32 PM13Oct 5-4:39 P
U. Houston - MATH - 3304
Derivatives HomeworkName: MyUH id number:Who helped you?Who did you help?Turn in the homework to 651 PGH; ask the receptionist to date stamp it and put it in my mailbox or Send it to me as a single pdf file by email.This is a 100 point as
U. Houston - MATH - 3304
Limits HomeworkName: PS id:This is a 112 point assignment. It WILL be on the mid-semester. Please turn it in personally in 651 PGH or via email in a single pdf file.1Problem 1 Why is limxa10 points x 2 + 6x + 5 21 ? = 2 x2 - 1 3Include a
U. Houston - MATH - 1314
Math 1314 Homework Assignment 000 Problem 4 Solve for x: ln( x 2 5) = 2
U. Houston - MATH - 1314
Math 1314 Homework Assignment 012 Problem 1 Suppose f ( x) = x 3 3 x 2 9 x + 27 . a. Find all rational zeros of the function and indicate their multiplicities. b. Use the guide to curve sketching to graph the function.
U. Houston - MATH - 1314
Math 1314 Assignment #15 1. At the beginning of a population study, there were 2.3 million people living in a major city. Five years later, the population had grown to 3.1 million people. a. Assuming exponential growth, what is the projected populati
U. Houston - MATH - 1314
Math 1314 Homework Assignment 018 1. Use Riemann sums, 4 subintervals and right endpoints to approximate the area under f ( x) = 3 x 2 + 5 on the interval [0, 8]. 2. Use Riemann sums, 4 subintervals and midpoints to approximate the area under f ( x)
NYU - B - 4000
Behavioral FinanceTerm: Prof.: Office: Office hours: Spring 2004 Jeffrey Wurgler (jwurgler@stern.nyu.edu) Tisch 9-09 (1) Tuesday 9-9:30pm and longer as needed (starting 1/27) (2) Thursday 1-1:30pm and longer as needed (starting 1/22) (3) Email for a
U. Houston - M - 1330
Simple Trigonometric Identities:1.cot = cos csc 2.tan = sin sec 1 sin2 x 3. = cos x cos x2 2 4. cos (tan + 1) = 15. cot x + tan x = sec x csc x
U. Houston - M - 1330
Solutions to the simple Trigonometric Identities:1.cot = cos csc cos sin 1 sin cos sin sin 1 cos 2.tan = sin sec sin cos 1 cos sin cos cos 1sin 1 - sin2 x 3. = cos x cos x cos 2 x cos xcos x2 2 4. cos (tan + 1) = 1
U. Houston - M - 1330
Review intermediate Trigonometric Identities:sin2 x 1. = sec x - cos x cos x2.cos sin + = sec2 - tan2 sec csc 2 2 2 4 3. 1 - cos 1 + cos = 2 sin - sin ()()4.1 = sec + tan sec - tan 5.cos x + 1 tan2 x=cos x sec x -
U. Houston - M - 1330
Solutions to the Intermediate Trigonometric Identities:sin2 x 1. = sec x - cos x cos x1 - cos 2 x cos x 1 cos 2 x - cos x cos x sec x - cos x2.cos sin + = sec2 - tan2 sec csc sin cos + 1 1 cos sin cos cos sin + sin 1 1work ot
U. Houston - M - 1330
Review Last Set of Trigonometry Identities: 1.1 + cos 1 - cos - = 4 cot csc 1 - cos 1 + cos 2.1 1 + = -2 tan tan - sec tan + sec 3.tan t - cot t = sec 2 t - csc 2 sin t cos t4.sin x sin x cos x - = csc x 1 + cos 2 x 1 - cos x 1
U. Houston - M - 1330
Solutions to the Review Last Set of Trigonometry Identities: 1.1 + cos 1 cos = 4 cot csc 1 cos 1 + cos (1 + cos )2 _ (1 cos )21 cos 2Get a common denominator1 + 2 cos + cos 2 1 2 cos + cos 2 sin2 1 + 2 cos + cos 2 1 + 2
U. Houston - M - 1314
Review for exam 2 M 1314:Find the limit: 1. x 3 2 x2 + 2 x 2x + 3 x 1 lim2. limx 32x2 4x2 x 12 3. lim x4 x44. limx +1 x 1 x 2 15.xlimx2 2x + 2 1 x36. lim2 5x x 6x + 1 x2 1 7. lim x x 18.Find the following
U. Houston - M - 1314
Review M1314test 31Review for test 3 M 1314: 1. Find the equation for the tangent line at a point: a. f ( x ) = 3x 2 - 6 x + 11at (- 1,2 )b. f ( x ) = e - x2 1 at 1, e2. Find the points on the graph of f at which the slope is a. - 4
U. Houston - M - 1314
M1314lesson 1 Math 1314 Lesson 1 Limits What is calculus?1The body of mathematics that we call calculus resulted from the investigation of two basic questions by mathematicians in the 18th century. 1. How can we find the line tangent to a curve
U. Houston - M - 1314
M1314Lesson 9 Math 1314 Lesson 9 Marginal Functions in Economics Marginal Cost1Suppose a business owner is operating a plant that manufactures a certain product at a known level. Sometimes the business owner will want to know how much it costs
U. Houston - M - 1314
M1314lesson 2 Math 1314 Lesson 2 One-Sided Limits and Continuity One-Sided Limits1Sometimes we are only interested in the behavior of a function when we look from one side and not from the other. Example 1: Consider the function f ( x) =x x .
U. Houston - M - 1314
M1314Lesson 10 Math 1314 Lesson 10 Applications of the First Derivative Determining the Intervals on Which a Function is Increasing or Decreasing From the Graph of f1Definition: A function is increasing on an interval (a, b) if, for any two num
U. Houston - M - 1314
M1314Lesson 18 Math 1314 Lesson 18 Area and the Definite Integral1We are now ready to tackle the second basic question of calculus the area question. We can easily compute the area under the graph of a function so long as the shape of the regi
U. Houston - M - 1314
M1314lesson 3 Math 1314 Lesson 3 The Derivative The Limit Definition of the Derivative1We now address the first of the two questions of calculus, the tangent line question. We are interested in finding the slope of the tangent line at a specifi
U. Houston - M - 1314
M1314lesson 11 Math 1314 Lesson 11 Applications of the Second Derivative Concavity1Earlier in the course, we saw that the second derivative is the rate of change of the first derivative. The second derivative can tell us if the rate of change o
U. Houston - M - 1314
M1314Lesson 19 Math 1314 Lesson 19 The Fundamental Theorem of Calculus1In the last lesson, we approximated the area under a curve by drawing rectangles, computing the area of each rectangle and then adding up their areas. We saw that the actual
U. Houston - M - 1314
M1314Lesson 4 Math 1314 Lesson 4 Basic Rules of Differentiation1We can use the limit definition of the derivative to find the derivative of every function, but it isn't always convenient. Fortunately, there are some rules for finding derivative
U. Houston - M - 1314
M1314Lesson 12 Math 1314 Lesson 12 Curve Sketching1One of our objectives in this part of the course is to be able to graph functions. In this lesson, we'll add to some tools we already have to be able to sketch an accurate graph of each functio
U. Houston - M - 1314
M 1314Lesson 20 Math 1314 Lesson 20 Evaluating Definite Integrals1We will sometimes need these properties when computing definite integrals. Properties of Definite Integrals Suppose f and g are integrable functions. Then: 1. 2. 3. 4. 5. a
U. Houston - M - 1314
M1314lesson 5 Math 1314 Lesson 5 The Product and Quotient Rules1In this lesson, we continue with more rules for finding derivatives. These are a bit more complicated. Rule 8: The Product Ruled [ f ( x ) g ( x )] = f ( x ) g ' ( x ) + g ( x) f
U. Houston - M - 1314
M1314Lesson 13 Math 1314 Lesson 13 Absolute Extrema1In earlier sections, you learned how to find relative (local) extrema. These points were the high points and low points relative to the other points around them. In this section, you will lear
U. Houston - M - 1314
M1314lesson 21 Math 1314 Lesson 21 Area Between Two Curves1Two advertising agencies are competing for a major client. The rate of change of the client's revenues using Agency A's ad campaign is approximated by f(x) below. The rate of change of
U. Houston - M - 1314
M 1314lesson 6 Math 1314 Lesson 6 The Chain Rule1In this lesson, you will learn the last of the basic rules for finding derivatives, the chain rule. Example 1: Decompose h( x) = 3 x 2 - 5 x + 6 into functions f (x) and g (x) such that h( x) = (
U. Houston - M - 1314
M 1314Lesson 14 Math 1314 Lesson 14 Optimization1Now youll work some problems where the objective is to optimize a function. That means you want to make it as large as possible or as small as possible depending on the problem. The first task is
U. Houston - M - 1314
M1314lesson 22 Math 1314 Lesson 22 Functions of Several Variables1So far, we have looked at functions of a single variable. In this section, we will consider functions of more than one variable. You are already familiar with some examples of th
U. Houston - M - 1314
M1314Lesson 7 Math 1314 Lesson 7 Higher Order Derivatives1Sometimes we need to find the derivative of the derivative. Since the derivative is a function, this is something we can readily do. The derivative of the derivative is called the second
U. Houston - M - 1314
M1314lesson 15 Math 1314 Lesson 15 Exponential Functions as Mathematical Models1In this lesson, we will look at a few applications involving exponential functions. Well first consider some word problems having to do with money. Next, well consi
U. Houston - M - 1314
M1314lesson 23 Math 1314 Lesson 23 Partial Derivatives1When we are asked to find the derivative of a function of a single variable, f (x), we know exactly what to do. However, when we have a function of two variables, there is some ambiguity. W
U. Houston - M - 1314
M 1314lesson 8 Math 1314 Lesson 8 Some Applications of the Derivative Equations of Tangent Lines1The first applications of the derivative involve finding the slope of the tangent line and writing equations of tangent lines. Example 1: Find the
U. Houston - MATH - 3303
Oct 12-3:52 PM1Oct 12-4:00 PM2Oct 12-4:04 PM3Oct 12-4:08 PM4Oct 12-4:12 PM5Oct 12-4:15 PM6Oct 12-4:18 PM7Oct 12-4:21 PM8Oct 12-4:28 PM9Oct 12-4:30 PM10Oct 12-4:32 PM11Oct 12-4:36 PM12Oct 12-4:42 PM13
U. Houston - MATH - 3303
Oct 26-3:52 PM1Oct 26-3:53 PM2Oct 26-4:05 PM3Oct 26-4:08 PM4Oct 26-4:11 PM5Oct 26-4:14 PM6Oct 26-4:16 PM7Oct 26-4:23 PM8Oct 26-4:28 PM9Oct 26-4:30 PM10Oct 26-4:33 PM11Oct 26-4:42 PM12Oct 26-4:52 PM13
U. Houston - MATH - 3303
Homework Module 4 3303 Name: email address: phone number:Who helped me:Who I helped:This is a 55 point assignment. Homework rules: Front side only. Keep the questions and your answers in order. If you send it pdf, send it in a single scanned
U. Houston - M - 1300
Math 1300 1. Homework is due before class begins. a. True b. FalsePopper 012. I must bubble in _ on popper scantrons or I will get a zero for that grade. a. Section number b. Assignment number c. Grading ID d. Form A e. All of the above 3. All te
U. Houston - M - 1300
Math 1300 1. Classify the number -2.5. a. Real b. Real, Rational c. Real, Rational, Integer d. Real, Irrational e. None of the above 2. Fill in the appropriate symbol: -9 _ -5. a. > b. < c. = d. None of the above 3. Add: -3 + (-5) a. -8 b. -2 c. 2 d.
U. Houston - M - 1300
Math 1300 1. Find the GCD of 28 and 42. a. 7 b. 14 c. 28 d. 84 e. None of the above 2. Find the LCM of 12 and 28. a. 4 b. 12 c. 28 d. 84 e. None of the above 3. Perform the given operation:a. b. c. d. e. 7 17 12 30 53 30 67 30 None of the above 3 6
U. Houston - M - 1300
Math 1300 1. Find the GCD of 28 and 42. a. 7 b. 14 c. 28 d. 84 e. None of the above 2. Find the LCM of 12 and 28. a. 4 b. 12 c. 28 d. 84 e. None of the above 3. Perform the given operation:a. b. c. d. e. 7 17 12 30 53 30 67 30 None of the above 3 6
U. Houston - M - 1300
Math 1300 1. Simplify: m4 m2. a. m2 b. m6 c. m8 d. m42 e. None of the above 2. Simplify: a. b. c.d. e.Popper 04x 2 y -2 x3x5 y2 x y2 1 5 2 x y 1 xy 2 None of the above3. Simplify 24x 2 a. 2x 6 b. 4x 6 c. 4x 3 d. 12x e. None of the above4.
U. Houston - M - 1300
Math 1300 1. Simplify: m4 m2. a. m2 b. m6 c. m8 d. m42 e. None of the above 2. Simplify: a. b. c.d. e.Popper 04x 2 y -2 x3x5 y2 x y2 1 5 2 x y 1 xy 2 None of the above3. Simplify 24x 2 a. 2x 6 b. 4x 6 c. 4x 3 d. 12x e. None of the above4.
U. Houston - M - 1300
Math 1300 1. Simplify: (2 + 4) 2 5 a. 31 b. 15 c. 7 d. 1 e. None of the above 2. Simplify: 2 3 + 15 3 a. 7 b. 11 c. 12 d. 16 e. None of the above c+b ? 3. If a = 2, b = -1, and c = 13, what is cb 6 a. 7 36 b. 49 49 c. 36 12 d. 14 e. None of the
U. Houston - M - 1300
Math 1300 1. Solve for x: 6x 13 = -5 a. -3 4 b. 3 c. 3 d. 2 e. None of the above2. Solve for x: 2(x + 3) = 6 a. -6 3 b. 2 c. 0 d. 3 e. None of the above 3. Write x < -3 in interval notation. a. (-, -3) b. (-, -3] c. [-3, ) d. (-3, ) e. None of the
U. Houston - M - 1300
Math 1300 1. Solve for x: 6x 13 = -5 a. -3 4 b. 3 c. 3 d. 2 e. None of the above2. Solve for x: 2(x + 3) = 6 a. -6 3 b. 2 c. 0 d. 3 e. None of the above 3. Write x < -3 in interval notation. a. (-, -3) b. (-, -3] c. [-3, ) d. (-3, ) e. None of the
U. Houston - M - 1300
Math 1300 1. Solve for x: (x + 3) = 6 a. 0 b. 3 c. 9 d. 15 e. None of the above 2. Solve for x: 2(x 5) = 3(x 2) 4 a. - 5 14 b. - 5 c. -4 d. -14 e. None of the above3. Write x 8 in interval notation. a. (-, 8) b. (-, 8] c. [8, ) d. (8, ) e. None o
U. Houston - M - 1300
Math 1300 1. Solve for x: (x + 3) = 6 a. 0 b. 3 c. 9 d. 15 e. None of the above 2. Solve for x: 2(x 5) = 3(x 2) 4 a. - 5 14 b. - 5 c. -4 d. -14 e. None of the above3. Write x 8 in interval notation. a. (-, 8) b. (-, 8] c. [8, ) d. (8, ) e. None o
U. Houston - M - 1300
1. a. b. c. d. e.Simplify the expression 16 - 8(6 + 2(-1) 3 ) -60 -28 -56 -24 None of the above1 x<6 62. Solve -a. b. c. d. e.(-, -1) (-, -36) (-1, ) (-36, ) None of the abovex 2 ( y 4 ) -1 3. Simplify z -3 z3 a. 2 4 x yb.x2 y4 z3 1 c.
U. Houston - M - 1300
1. a. b. c. d. e.Simplify the expression 16 8(6 + 2(1) 3 ) -60 -28 -56 -24 None of the above1 x<6 62. Solve a. b. c. d. e.(-, -1) (-, -36) (-1, ) (-36, ) None of the above( x 2 y 4 ) 1 3. Simplify z 3 z3 a. 2 4 x y b.x2 y4 z3 1 c. 2 4 3
U. Houston - M - 1300
Math 1300Popper 09 02/20/09Solve each of the following: 1. -3(4 + 5x) < -2(7 x) a. (-, 2/17) b. (2/17, ) c. (-, 2/17] d. [2/17, ) e. None of the above 2. -9 < 2x 3 < 13 a. (-3, 8) b. (-6, 5) c. (-, -3) u (8, ) d. (-, -6) u (5, ) e. None of the
U. Houston - M - 1300
Math 1300Popper 09 02/20/09Solve each of the following: 1. -3(4 + 5x) < -2(7 x) a. (-, 2/17) b. (2/17, ) c. (-, 2/17] d. [2/17, ) e. None of the above 2. -9 < 2x 3 < 13 a. (-3, 8) b. (-6, 5) c. (-, -3) u (8, ) d. (-, -6) u (5, ) e. None of the