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by: Anna Kolar

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# Schaum's Chapter 2 Notes for Math Quiz 1 CS200

Marketplace > Boston University > Computer science > CS200 > Schaum s Chapter 2 Notes for Math Quiz 1
Anna Kolar
BU

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These notes cover Schaum's College Algebra Chapter 2 which will be included in Math Quiz 1 for Module 1
COURSE
Fundamentals of Information Technology
PROF.
Bragg
TYPE
Class Notes
PAGES
3
WORDS
CONCEPTS
Algebra, Algebraic, Expression, term, monomial, multinomial, coefficient, numerical, literals, polynomials, constant, grouping, simplify
KARMA
25 ?

## Popular in Computer science

This 3 page Class Notes was uploaded by Anna Kolar on Saturday September 10, 2016. The Class Notes belongs to CS200 at Boston University taught by Bragg in Fall 2016. Since its upload, it has received 15 views. For similar materials see Fundamentals of Information Technology in Computer science at Boston University.

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Date Created: 09/10/16
Schaum’s College Algebra Fourth Edition – Chapter 2 – Module 1 Fundamental Operations with Algebraic Expressions Term Definition Example Secti on Algebraic expression A combination of ordinary numbers and letters with represent numbers 3a + 4b 2.1 Term Products and quotients of ordinary numbers and letters which represent numbers 3a 2.1 3 4 Monomial Algebraic expression with just one term (and are occasionally just called terms) 7a b 2.1 Multinomial Algebraic expression with more than one term 3a + 4b 2.1 Coefficient One factor of a term In 7a , the coefficient is 7 2.2 In 7a b , y, a , and b are  coefficients 3 Numerical coefficient If one number is being multiplied by one or more letters, the number is considered the  In 7a , the numerical  2.2 numerical coefficient (or just the coefficient) coefficient is 7 Like/Similar terms Terms that only differ by numerical coefficients; these can be combined by adding the  7a and 9a 3 2.2 coefficients together and create one term Literals Letters which represent numbers 2.2 Polynomial A molnomial/multinomial where each term is integral and rational 3 4  2.2 Degree of a monomial Sum of all exponents The degree of 7a b is 7 2.3 Degree of a polynomial Equal to the term with the largest degree 7a b + 3xy + 2a c  = 7, 2, and  2.3 6 so the degree is 7 Constant Singular number 6, Pi, 0, ­3 2.3 Degree of a constant Always 0 2.4 Grouping symbols Parenthesis (), brackets [], and braces{} 2.4 Grouping Shows that terms contained in them are a single quantity 2.4 + sign preceeds a  Remove the grouping without any change 2.4 grouping ­ precedes a grouping Change the sign of each term before removing the grouping (3a + 4b) – (5c + 6d ­7e) 2.4 = 3a + 4b ­5c – 6d +7e Groupings within  Start on the innermost grouping and move out ([{}]) In this case, braces, then 2.4 groupings brackets, then parenthesis Addition of algebraic  Combine like terms by arranging into columns 3a + 5b+6c 2.5 expressions 1a – 2b ­5c = 4a+3b+c Multiplying monomials Use laws of exponents, rules of signs, and ammutative/associative properties of  (3ab)(2a b )(a bc ) 2 5 3 6 multiplication = (3*2*1)(a*a *a )(b*b *b)(c ) = Schaum’s College Algebra Fourth Edition – Chapter 2 – Module 1 Fundamental Operations with Algebraic Expressions 8 5 6 6a b c Multiplying monomials Multiply each term of the polynomial by the monomial and simplify (5a b )(2ab + 5b) and polynomails = [(5*2)(a *a)(b *b)] + [(5*5)(a) (b *b)] = 10a b +25ab 3 Multiplying two  Multiply each of the terms of one polynomial by each of the terms of the other polynomials     (­2a + 5b) polynomials and combine (6+a) 2 =­12a+30b ­2a +5ab 2 5 7 2 4 Dividing monomials by 1. Divide numerical coefficients 30a b cd  / 2ab c monomials 2. Divide variables = 3. Multiply the quotients 2 5 2 4 7 (30/2)(a /a)(b /b )(c/c )(d ) = 3 ­3 7 15ab c d = 3 7 15ab d C3 Dividing polynomials  1. Arrange in descending or ascending powers (your pick) by one of the variables  Dividend/divisor =  by polynomials found in both polynomials Quotient + (remainder/divisor) 2. Divide the first in the dividend by the first term in the divisor (which gives the first  quotient term) See example on page 15 to see 3. Multiply the first term in the quotient by the divisor and subtract from the dividend  a full problem worked out (this gives you a new dividend) 4. Use this dividend and repeat steps 2 and 3 until a remainder is obtained Example problems: Page 16­20 2.1 Evaluate the algebraic expression where X=1, y=2, z=3 2x +4xy –z 2 2(1)+4(1)(2)­(3) 2 = 2+8­9 =1 2 2.2 Classify algebraic expressions as a term/monomial, binomial,  X +2xy Binomial, multinomial, polynomial trinomial, multinomial, or polynomial X /2xy Monomial 2 2 X  + 2xy + 4xy z Trinomial, multinomial, polynomial X  + 2xy + √4xy z 2 Trinomial, multinomial Schaum’s College Algebra Fourth Edition – Chapter 2 – Module 1 Fundamental Operations with Algebraic Expressions 2 2 X  + 2xy + 4xy z + z Multinomial, polynomial 2.3 Find the degree of a polynomial X  + 2xy + 4xy z + z 2, 2, 4, 1 – The degree is 4 X + 5 4 2 – the degree of the constant is 0 2 2 2.4 Remove the symbols of groupings and simplify by combining like  X  + 2xy + 4(3x – 2y) +4xy z ­(6xy  terms +3x )2 2 2 2 = x  +2xy+12x­8y+4xy z­6xy­3x =­2x ­4xy+12x­8y+4xy z 2 2.5 Adding algebraic expressions See page 17 (too complicated to type) 2.6 Subtracting algebraic expressions See page 17 (too complicated to type) 2.7 Product of algebraic expressions See page 18 (too complicated to type) 2.8 Dividing algebraic expressions See page 18 (too complicated to type) 2.9 Checking work by evaluating algebraic expressions Check your work in the previous two  problems using the methods of example  problem 2.1

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