Algebra: Understanding Terms, Polynomials, and Degrees

Communicate with Algebra A term is an expression formed by the product of numbers and/or variable. Exercise 1: Identify the coefficient and the variable of each term a)8x Coefficient: 8 , Variable: x b) Coefficient: -4.9 , Variable: − 4. 9𝑡 2 𝑡 2 c) 1/2 bh Coefficient: 1/2 , Variable: bh d) Coefficient: 1 , Variable: 1𝑘 2 𝑘 2 A Polynomial is an algebraic expression consisting of one or more terms c onnected by addition or subtraction operators. A Polynomial can be classified by the number of terms it has or by its degr ee. Type of Polynomial Number ofTerms Examples Monomial 1 𝑥 2 , − 2𝑥 3𝑦 5 Binomial 2 𝑥 2 + 𝑦 2 , 2𝑥 3𝑦 − 5𝑥𝑦 4 trinomial 3 𝑥 2 − 𝑥𝑦 + 𝑦 2 , 3𝑥 2 − 𝑥𝑦 +

Exercise 2: Classify each polynomial by the number of terms it has. Polynomial Number ofTerms Type of Polynomial 3𝑥 2 + 2𝑥 2 Binomial − 2𝑚 1 Monomial 4𝑥 2 − 3𝑥𝑦 + 𝑦 2 3 trinomial 𝑎 − 2𝑏 + 𝑐 − 3 4 Polynomial with fourterms Degree of a term is the SUM of the exponents on the variables in a term Exercise 3: Find the degree of each term a) 𝑥 2 Degree: 2 b) 3𝑦 4 Degree: 4 c)0.7u Degree: 1 d) − 2 𝑎 5 𝑏 2 𝑐 6

Degree: 13 e) -5 Degree: 0 Degree of a polynomial is the degree of the highest-degree term. Exercise 4 : Find the degree of each polynomial Polynomial Term with highestdegree Degree of Polynomial 𝑥 + 3 𝑥 4 1 5𝑥 2 − 2𝑥 𝑥 2 2 𝑦 3 + 0. 2𝑦 − 1 𝑦 3 3 7𝑥 2 𝑦 4 + 𝑥 6 𝑦 𝑥 6 𝑦 7 Example 5 : A hockey team earns 2 points for a win and 1 point for a tie. a)Write an expression that describes the total number of points the team can earn. b) Write let statements to identify what the variables represent. c) How many points will a team earn if they win 5 games and tie 3? Solution: a)2x+1y OR 2x+y

b) Let x represent the number of games won and let y represent thenumber of games tied. c) Replace x by 5 and y by 3. (x=5 and y=3) 2x+y=2(5)+3 =10+3 =13 A team that won five games and tied three games will have 13 points.