University:
Missouri State University
Course:
MTH 103 | Intermediate Algebra
Academic year:

2019
Views:

228

Pages:

2
Author:

ke1ra3p2uaper

Lesson 10.1 Notes: Adding and Subtracting Polynomials Polynomial Vocabulary: 1) A polynomial is an expression with one or more terms. If the expression has exactly one term, it is called a nonomial binomial A polynomial that has two terms is called a while a polynomial that has three terms is called a trinomial 2) The different parts or pieces of a polynomial are called the terms the same variables and the same exponents, they are called like If those terms have terms. If the term has a variable, the number multiplying (directly in front of the variable) is called the Coefficient If the term does not have a variable, it is called a constant 3) All polynomial expressions should be written in Standard form meaning that the terms are placed in de descending. order (exponents go from highest to lowest). Vocabulary Examples: 1. Determine whether each polynomial is a monomial, binomial, or trinomial. A) 4x ^ 3 - 8x binomial B) -5xy monomial C) x ^ 2 - 2x + 1 trinomial 2. Determine whether each of the following pairs are like terms. Write yes or no A) 6x ^ 2, x ^ 2 yes B) 9x .-3y no-variah. C) 8x * 0.2x ^ 3 no-expon. D) 2xy.-3yx y >= 5 - 3xy 3. For each of the following expressions, identify the coefficients and the constants. A) 7x + 1 B) - 4x ^ 2 * y + 0 C) -9 Ox-9 D) x ^ 2 - 5x + 4 Coefficents: 7 Coefficents: -4 Coefficents: Coefficents: 1, 5 Constants: Constants: Constants: -9 Constants: 4 4. Write the following polynomials in standard form. Then state the degree of the polynomial. A) - 2x + x ^ 2 - 3 B) 8 - 7x C) x - 9x ^ 4 + 6x ^ 2 - x ^ 3 Standard form: x ^ 2 - 2x - 3 Standard form: - 7x + 8 Standard form: - 9x ^ 4 - x ^ 3 + 6x ^ 2 + x Degree 2 Degree: Degree: 4 Adding and Subtracting Polynomials: You can only add or subtract the like terms. When adding/subtracting like terms, you only add/subtract the coefficients. Do not add the exponents! You can use either a horizontal format or a vertical format. Write your final answer in standard form. Examples: 5) ( 4x[- 3) + (7x) + 81 11x + 5 6) (3x - 4) - (2x + 6) 3426 x - 10 7) (4x)-8x+3)+ (2x)|12x| - 5 ) 6x ^ 2 + 4x - 2 8) (5x -1)+ boxed (6x - 9x ^ 2 ) - 4x ^ 2 + 6x - 1 9) (x ^ 2 - 8) - (7x + 4x ^ 2) x ^ 2 - 8 - 7x(4x ^ 2) - 3x ^ 2 - 7x - 8 10) (5x ^ 3 - x + 2x ^ 2) + (7 - 4x) - (6x ^ 2 + 5x ^ 3 - 3) 4x6x - 4x ^ 2 - 5x + 10 11) 2x ^ 2 + x - 5 (+ h * x ^ 2 + x + 6 3x ^ 2 + 2x + 1 12) - 2x ^ 3 + 5x ^ 2 - x + B (+) + 2x ^ 3 + 3x -^ 7 +4 5x ^ 2 - 4x + 12 Multiple Choice Practice: 13) Solve: |3x - 4| = 8 A) x = 4 B) x = 4/3 C) \{4, - 1/3\} D) \{4/3, - 4\} 3x - 4 = 8 3x = 12 x = 4 3x - 4 = - 8 3x = - 4 x= - 11/3