Answer Key
University
High SchoolCourse
MPM1D | Principles of MathematicsPages
4
Academic year
2023
anon
Views
24
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: β 4. 9π‘ 2 π‘ 2 c) 1/2 bh Coefficient: 1/2 , Variable: bh d) Coefficient: 1 , Variable: 1π 2 π 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 π₯ 2 , β 2π₯ 3π¦ 5 Binomial 2 π₯ 2 + π¦ 2 , 2π₯ 3π¦ β 5π₯π¦ 4 trinomial 3 π₯ 2 β π₯π¦ + π¦ 2 , 3π₯ 2 β π₯π¦ +
Exercise 2: Classify each polynomial by the number of terms it has. Polynomial Number ofTerms Type of Polynomial 3π₯ 2 + 2π₯ 2 Binomial β 2π 1 Monomial 4π₯ 2 β 3π₯π¦ + π¦ 2 3 trinomial π β 2π + π β 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) π₯ 2 Degree: 2 b) 3π¦ 4 Degree: 4 c)0.7u Degree: 1 d) β 2 π 5 π 2 π 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 π₯ + 3 π₯ 4 1 5π₯ 2 β 2π₯ π₯ 2 2 π¦ 3 + 0. 2π¦ β 1 π¦ 3 3 7π₯ 2 π¦ 4 + π₯ 6 π¦ π₯ 6 π¦ 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.
Algebra: Understanding Terms, Polynomials, and Degrees
Please or to post comments