Polynomials: Basic Operations and Factoring Mathematics 17 Institute of Mathematics Lecture 3 Math 17 (Inst. of Mathematics) Polynomials: Basic Operations and Factoring Lec 3 1 / 30 Outline 1 Algebraic Expressions and Polynomials Addition and Subtraction of Polynomials Multiplication of Polynomials Division of Polynomials 2 Factoring Sum and Difference of Two Cubes Factoring Trinomials Factoring By Grouping Completing the Square Math 17 (Inst. of Mathematics) Polynomials: Basic Operations
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Department of Career & Professional Development Winter 2014 Final Examination — with answers Student Name Student Number Foundations of Mathematics CMSC 000 Lecturer: G. Brown Date: Time: 17 April 2014 3 hours INSTRUCTIONS: This is a closed book examination. Give your answers in the exam booklet. You are permitted non-electronic translation dictionaries only. Handheld devices capable of storing text are NOT permitted. Calculators are permitted. Only noiseless non-programmable calculators
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Read the following instructions in order to complete this discussion‚ and review the example of how to complete the math required for this assignment: Write your birth date or the birth date of someone in your family as mm/dd/yy. (Example: March 13‚ 1981 is written 3/13/81‚ and November 7‚ 1967 is written 11/7/67). Now let a = the one- or two-digit month number‚ b = the negative of the one- or two-digit day number‚ and c = the two-digit year number.
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Algebra What is Algebra? Algebra is a part of mathematics in which symbols such as letters of the alphabet (also known as pro-numerals) stand for numbers. Instead of guessing whether we are to call it a hundred‚ or six‚ or a thousand and sixty four‚ why not just call it x. This method of solving problems is called Algebra. Important People and Dates Relating to Algebra Algebra was developed to solve difficult logic/math problems. It all began in ancient Egypt and Babylon‚ where people
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Algebra II 7.3 Binomial Radical Expressions Radical expressions with the same index and the same radicand may be added or subtracted. Add or subtract: May need to simplify before adding or subtracting. Assignment: page 382383‚ #112 7.3 continued Multiplying Binomial Radical Expressions Use FOIL to multiply‚ simplify. Multiply: Conjugates are expressions such as: Just as (ab)(a+b) = a2b2 The product of conjugates is a rational number. Simplify: Assignment: page 382383‚ # 1322 7
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COMPETENCY 2 1). Simplify the expression by combining like terms. 5x - y - 2x + 3y a) 3x + 2y b) 2x –y c) x - y d) None of these 2. Use the distributive property to evaluate the expression. 3( x – 3 – 2y) a) 3x - 9 + 2y b) x –y c) 3x - 9 -6y d) None of these 3. Perform the indicated operation: a) b) c) d)
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CHAPTER 4: VARIABLES AND ARITHMETIC OPERATION 1. Name three numeric data types that can contain a decimal point. 2. Write a Dim statement for each of the following variables using the variable type and variable name that would be best for each value. a. Population of the Philippines b. Your weekly baon c. The smallest data type you can use for your age. d. A constant for the first initial of your first name e. The minimum allowance in a month f. The name of the city in which you live g. The answer
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Simplifying Expressions 2a(a-5)+4(a-5) The given expression. a*2 Multiply a and 2. 2a^2 2*a*2 = 2a^2. 2a^2*a-5 The distributive property removes the parenthesis. 2a × -5 = -10a Multiply 2a by -5=-10a. -10a 2a^2-10a + 4(a-5) Use the distributive property to remove the parentheses. 4*a= 4a 4*-5= -20 Multiply 4 by a-5. 4 × a = 4a 4*-5=-20 Multiply 4 by a‚ and 4 by -5 4a-20 2a^2-10a + 4a -20 Add the coefficients; combine like
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Class -8 Factorization MLP 1. Factorise the following expressions: (i) 7x – 42 (ii) 6p − 12q (iii) 7a2 + 14a (iv) −16z + 20z3 (v) 20 l2 m + 30 a l m (vi) 5x2y − 15xy2 (vii) 10a2 − 15b2 + 20c2 (viii) −4a2 + 4ab − 4 ca (ix) x2 y z + xy2 z + xyz2 (x) ax2 y + bxy2 + c xyz 2. Factorize: (i) x2 + x y + 8x + 8y (ii) 15xy − 6x + 5y – 2 (iii) ax + b x − ay – by (iv)15pq + 15 + 9q + 25p (v) z − 7 + 7xy – xyz 3. Add: 7xy + 5yz – 3 z x ‚ 4yz + 9zx – 4 y
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MATH 1003 Calculus and Linear Algebra (Lecture 1) Albert Ku HKUST Mathematics Department Albert Ku (HKUST) MATH 1003 1 / 18 Outline 1 About MATH 1003 2 Mathematics of Finance 3 Simple Interest Albert Ku (HKUST) MATH 1003 2 / 18 About MATH 1003 About MATH 1003 Lecturer: Albert Ku (Office: Rm 3492. E-mail: maybku@ust.hk) Teaching assistant: Dy Chun Yin‚ Li Xing‚ Lau Hing Sang and Wong Kwok Pang Office hours at Learning Commons: Fri 10:00-noon Textbook:
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