Wed 32210 SWBATidentify the difference between monomials binomials
Wed, 3/22/10 SWBAT…identify the difference between monomials, binomials and trinomials and the degree of each. Agenda 1. 2. 3. WU (5 min) Quiz (10 min) Correct quiz (5 min) WARM-UP 1. Questions before we start the quiz? Study for quiz
Polynomials A polynomial is a monomial or the sum or difference of monomials n Some polynomials have special names: n ¨A binomial is the sum or difference of two monomials ¨ A trinomial is the sum or difference of three monomials
Expression 4 y – 5 xz -6. 5 7 a-3 + 9 b 6 x 3 + 4 x + 3 Is it a polynomial? Monomial, binomial, or trinomial?
Expression 4 y – 5 xz -6. 5 7 a-3 + 9 b 6 x 3 + 4 x + 3 Is it a polynomial? Yes; 4 y – 5 xz is the difference of two monomials. Monomial, binomial, or trinomial? Binomial
Expression 4 y – 5 xz -6. 5 7 a-3 + 9 b 6 x 3 + 4 x + 3 Is it a polynomial? Yes; 4 y – 5 xz is the difference of two monomials. Yes; -6. 5 is a constant Monomial, binomial, or trinomial? Binomial Monomial
Expression 4 y – 5 xz -6. 5 7 a-3 + 9 b 6 x 3 + 4 x + 3 Is it a polynomial? Monomial, binomial, or trinomial? Yes; 4 y – 5 xz is the difference of two monomials. Yes; -6. 5 is a constant Binomial No; 7 a-3 = , which is not a monomial None of these Monomial
Expression 4 y – 5 xz -6. 5 7 a-3 + 9 b Is it a polynomial? Monomial, binomial, or trinomial? Yes; 4 y – 5 xz is the difference of two monomials. Yes; -6. 5 is a constant Binomial No; 7 a-3 = , which is not a monomial None of these 6 x 3 + 4 x + 3 Yes; 6 x 3 + 4 x + 3 = 6 x 3 + 5 x + 3, the sum of three monomials Monomial Trinomials
Degree of a monomial The degree of a monomial is the sum of the exponents of all its variables. Ex: 3 a 2 b 3 Degree = 2 + 3 = 5 n ¨A nonzero constant has degree 0. Ex: 7 Degree = 0 ¨ Zero has no degree
Degree of a polynomial n The degree of a polynomial is the greatest degree of any term in the polynomial. ¨ To find the degree of a polynomial, you must find the degree of each term. Ex. 2 d 3 – 5 c 5 d – 7 Step 1: Find the degree of each term 2 d 3: Degree = 3 5 c 5 d: Degree = 5 + 1 = 6 7: Degree = 0 Step 2: The degree of polynomial is the greatest degree, 6.
OYO Problems Directions: Find the degree of each polynomial: 1. 2. 3. 4. 5. 7 xy 5 z 2 rt – 3 rt 2 – 7 r 2 t 2 – 13 9 x 2 – 2 x – 4 12 + 5 b + 6 bc + 8 bc 2 -4 Answers: 1. 7 2. 4 3. 2 4. 3 5. 0
Some polynomials have special names based on their degree. Degree Name 0 Constant 1 Linear 2 Quadratic 3 Cubic 4 Quartic 5 Quintic 6 6 th degree, 7 th degree, and so on
Polynomials in Standard Form The standard form of a polynomial is written with the terms in order from greatest degree to least degree. n When the polynomial is written in standard form, the coefficient of the first term is called the leading coefficient. n
Write each polynomial in standard form. Identify the leading coefficient. Ex 1: 3 x 2 + 4 x 5 – 7 x Answer: 4 x 5 + 3 x 2 – 7 x The leading coefficient is 4 Ex 2: 5 y – 9 – 2 y 4 – 6 y 3 Answer: – 2 y 4 – 6 y 3 + 5 y – 9 The leading coefficient is -2
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