University:
High School
Course:
High School Mathematics
Academic year:

2022
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190

Pages:

3
Author:

pasiweb2yv

Adding & Subtracting Polynomials Vocabulary Monomial: Is a single term polynomial. Example: 7a, a, 9, 7a^2b^4 Degree of a Monomial: The sum of the exponents of all the variables. Examples: 7a (degree 1), a (degree 1), 9 (degree 0), 7a^2b^4 (degree 6) Polynomial: Terms/expressions put together. Binomial: Is a 2-term polynomial. Example: 7a + b, 5x - yhv Trinomial: Is a 3-term polynomial. Example: 5x^3 - 7a + a^2x^4 Degree of a Polynomial: Is the biggest term degree. Example: 3x^3 + 7a + a^2x^4 (degree 4) Standard Form: Write the polynomial highest degree first. Example: a^2x^4 + 5x^3 - 7a Leading Coefficient: The # in front of the leading term. Core Concepts Polynomials: A polynomial is a monomial or a sum of monomials. Each monomial is called a term of the polynomial. A polynomial with two terms is a binomial. A polynomial with three terms is a trinomial. Examples: Binomial (5x + 2), Trinomial (x^2 + 5x + 2) The degree of a polynomial is the greatest degree of its terms. A polynomial in one variable is in standard form when the exponents of the terms decrease from left to right. When you write a polynomial in standard form, the coefficient of the first term is the leading coefficient. Example: 2x^3 + x^2 - 5x + 12 Section 1: Find the degree of the monomial. -68 Degree: 0 w Degree: 1 8 Degree: 0 -2abc Degree: 3 7x²y Degree: 2 + 1 = 3 4r²s²t Degree: 2 + 2 + 1 = 5 10mn³ Degree: 1 + 3 = 4 2/3 Degree: 0 You Try -3x⁴ Degree: 4 7c³d⁸ Degree: 3 + 8 = 11 5/3y Degree: 1 -20.5 Degree: 0 Section 2: Identifying and Classifying Polynomials In Exercises 9-12, write the polynomial in standard form. Identify the degree and leading coefficient of the polynomial. Then classify the polynomial by the number of 1 terms. 1. www.scribd.com www.scribd.com x + 3x² + 5 Standard Form: 3x² + x + 5 Degree: 2 Leading Coefficient: 3 Classify: Trinomial √5y Standard Form: √5y Degree: 1 Leading Coefficient: √5 Classify: Monomial 3x³ + 6x⁸ Standard Form: 6x⁸ + 3x³ Degree: 8 Leading Coefficient: 6 Classify: Binomial f² - 2f + f⁴ Standard Form: f⁴ + f² - 2f Degree: 4 Leading Coefficient: 1 Classify: Trinomial You Try 4 - 9z Standard Form: -9z + 4 Degree: 1 Leading Coefficient: -9 Classify: Binomial t² - t⁴ - 10t Standard Form: -t⁴ + t² - 10t Degree: 4 Leading Coefficient: -1 Classify: Trinomial 2.8g + g³ Standard Form: g³ + 2.8g Degree: 3 Leading Coefficient: 1 Classify: Binomial