Download presentation

Presentation is loading. Please wait.

Published byChristopher Pope Modified over 7 years ago

1
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 3.3 Introduction to Polynomials

2
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 22 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Defining Term and Coefficient Term – a number or a product of a number and variables raised to powers Coefficient – numerical factor of a term Constant – term which is only a number Polynomial is a finite sum of terms of the form ax n, where a is a real number and n is a whole number.

3
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 33 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. In the polynomial 7x 5 + x 2 y 2 – 4xy + 7 There are 4 terms: 7x 5, x 2 y 2, – 4xy and 7. The coefficient of term 7x 5 is 7, of term x 2 y 2 is 1, of term –4xy is –4 and of term 7 is 7. 7 is a constant term. Defining Term and Coefficient

4
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 44 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Monomial is a polynomial with exactly one term. Binomial is a polynomial with exactly two terms. Trinomial is a polynomial with exactly three terms. Types of Polynomials

5
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 55 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. The degree of a term in one variable is the exponent on the variable. The degree of a constant is 0. The degree of a polynomial is the greatest degree of any term of the polynomial. The degree of 9x 3 – 4x 2 + 7 is 3. The degree of a term with more than one variable is the sum of the exponents on the variables. The degree of the term 5a 4 b 3 c is 8 (remember that c can be written as c 1 ). Degrees

6
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 66 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Evaluating a polynomial for a particular value involves replacing the value for the variable(s) involved. Find the value of 2x 3 – 3x + 4 when x = – 2. = 2( – 2) 3 – 3( – 2) + 42x 3 – 3x + 4 = 2( – 8) + 6 + 4 = – 6 Evaluating Polynomials Example

7
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 77 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Like terms are terms that contain exactly the same variables raised to exactly the same powers. Combine like terms to simplify. x 2 y + xy – y + 10x 2 y – 2y + xy Only like terms can be combined through addition and subtraction. Warning! = 11x 2 y + 2xy – 3y = (1 + 10)x 2 y + (1 + 1)xy + (– 1 – 2)y = x 2 y + 10x 2 y + xy + xy – y – 2y Group like terms. Combining Like Terms Example Use the distributive property. Simplify.

Similar presentations

© 2023 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google