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# BASIC COLLEGE ALGEBRA MAC 1105

UF

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This 10 page Class Notes was uploaded by Marquise Graham on Saturday September 19, 2015. The Class Notes belongs to MAC 1105 at University of Florida taught by Staff in Fall. Since its upload, it has received 21 views. For similar materials see /class/207049/mac-1105-university-of-florida in Calculus and Pre Calculus at University of Florida.

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Date Created: 09/19/15

L3 Polynomial Division Synthetic Division Rational Expressions Long Division 15 5426 15 426 2 Check Dividend QuotientDivisor Remainder Dividing by a monomial 4x5 6x3 x2 2x2 2x2 l4x5 6x3 x2 21 Dividing Two Polynomials with more than One Term 1 Write terms in each polynomial in descending order according to degree 2 Insert missing terms in both polynomials with a O coefficient 3 Use Long Division algorithm The remainder is a polynomial whose degree is less than the degree of the diVisor Example Perform the diVision 3x4 6x2 12x 4 3x2 2 3x2 0x 23x4 Ox3 6x2 l2x 4 22 Synthetic Division Synthetic division is used when a polynomial is divided by a firstdegree binomial of the form x k 0m2 bx c x k k a b c Coefficients of Dividend Diagonal pattern Multiply by k Vertical pattern Add terms Example Use synthetic division to find the quotient and remainder 2x4 3x2 5xl xl 23 Example Verify that x 3 is a factor of x3 x2 10x 6 Rational Expressions A rational expression is a ratio of two polynomials The domain of an expression in one variable is the set of all real numbers for which the expression is defined The domain of a rational expression is the set of all real numbers that do not make the denominator equal to zero Reducing Rational Expressions z if 97200720 bc 9 24 Example Find the domain and reduce the expression to lowest terms x25x6 l 3x9 Domain x2 25 2 5 x Domain Multiplication and division 233 ifb 0d 0 b d bd i ifb 00 0d 0 b d b c 25 Example Perform the indicated operations and simplify Give restrictions on the variables 4y 2y3 y2 5y6 XZ yZJX yf xy 39 W 26 Addition and subtraction In order to add subtract rational expressions we use the Least Common Multiple LCM of the denominators To Find the LCM of the Denominators 1 Factor polynomials that are in the denominators 2 The LCM is the product of all different factors which are in the denominators numbers variables expressions each raised to the largest power that appears on that factor Example Add or subtract as indicated Give all restrictions on the variables x x 3 3x2 x 2x3 x2 27 Note Be aware of the case when the denominators are additive inyerses of each other Example Perform the indicated operations 2 5 3x 5x x2 x 2 Mixed Quotients A mixed quotient complex fraction is a quotient of rational expressions Simplifying a Complex Fraction Method 1 Multiply both numerator and denominator by the LCM of the denominators of all simple fractions and simplify Method 2 Perform the indicated additions andor subtractions in the numerator and denominator and then divide 28 Example Simplify the complex fraction mixed quotient 1L x1 231 X 11 x x1 x1 29 Example Write the fraction as a sum of two or more expressions x3 5x2 4 x2 Example Perform the indicated operations and simplify i ch2 x2 h 30

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