Lesson 24, Section 5.1PolynomialsDefinition: A term is a number, a variable, a power of a variable, or the product of any of these. A term is also commonly called a monomial.Examples: 2443xyxwDefinition: A Polynomial is a sum (or difference) of Terms (monomials).Examples: 322334424324babaxxxyxDefinition: A Binomial is a polynomial of two terms. A Trinomial is a polynomial of three terms.Binomial Examples: axxy34232Trinomial Examples: ababrr 5342Definition: The Degree of a monomial (or term) is the sum of its exponents of the variables.Examples with degrees: 0 degree 47 degree 34 degree 75 degree 45225xyzyxxDefinition: The Coefficient of a monomial (or term) is the number factor.Examples and coefficients: 23t coefficien 231t coefficien 5t coefficien 52xyxxyThe Leading Term of a Polynomial is the term of the highest degree. Its coefficient is called the Leading Coefficient. The degree of the polynomial is the degree of the leading term. The degree of a constant (number) is zero.11) List the terms, the degree of each term, the coefficient of each term, the leading term, and the degree of the polynomial.xxyyxx 127642335Terms:54x336 yx27xyx12Degrees:Coefficients:Leading Term: Degree of the Polynomial:Generally a polynomial of one variable is written in descending order of powers. (Occasionally, directions may state to write in ascending order.)2) Write in descending order of powers.3425213234 xxxxx Definition: A Polynomial Function is of the form )(xPa polynomial.Examples: 245)(23)(143)(35242rrrGtttPxxxf3) Evaluate this polynomial function for x = -2.xxxxP 234)(234) Evaluate g(-1) if 7524)(23 xxxxg.To add or subtract polynomials, combine 'like' terms.5) Add 6433 xx and 1027423 xxx.26) Subtract xxx 2343 from 423 xx.7)222.443541.36532xxyxxxxy8))82()127()23195(222 xxxxxx9))86()247()59( trtwrtwr 10))749()3410(2222xyyyxyyxxy Application Examples:11) The number of milligrams (M(t)) of ibuprofen in the bloodstream for t hours after swallowing a 400 mg tablet is given bytttttM 7.34765.9645.35.0)(234 for 60 t. (Source: Dr. P. Carey, Burlington, VT)3How many milligrams are in the bloodstream in 2 hours after a 400 mg tablet is swallowed?12) The speed v(t) in miles per hour at which a diver enters the water after diving is approximated by ttv 82.21)( where t is number of seconds of falling. (Source: www.guinnessworldrecords.com) A diver in Acapulco, Mexico is in the air for 5 seconds. What is the speed at which he enters the water?In business, total profit is total revenue minus total cost. If functions can be determined for profit, revenue, and cost; then )()()( xCxRxP .13) If the revenue of a company selling x futons is 27.0280)( xxxR and the costof making x futons is 25.08000)( xxC , find the profit function and the profit from the sale of 200
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