Math "Adding and Subtracting Polynomials" Bibiana Lopez. July Riverside City College. (RCC) 10.1 July / 15

Transcription

1 Math "Adding and Subtracting Polynomials" Bibiana Lopez Riverside City College July 2010 (RCC) 10.1 July / 15

2 Objectives: * Add and subtract polynomials. * Evaluate polynomials at given replacement values. (RCC) 10.1 July / 15

3 Preliminaries: Before we add and subtract polynomials, we need to review some definitions presented in Section 3.1. The addends of an algebraic expression are called the terms of the expression. (RCC) 10.1 July / 15

4 Preliminaries: Before we add and subtract polynomials, we need to review some definitions presented in Section 3.1. The addends of an algebraic expression are called the terms of the expression. For example, 3x + 5 (Two terms), 7y 2 + ( 6y) + 4 (Three terms). (RCC) 10.1 July / 15

5 Preliminaries: Before we add and subtract polynomials, we need to review some definitions presented in Section 3.1. The addends of an algebraic expression are called the terms of the expression. For example, 3x + 5 (Two terms), 7y 2 + ( 6y) + 4 (Three terms). A term that is only a number has a special name. It is called a constant term, or simply a constant. (RCC) 10.1 July / 15

6 Preliminaries: Before we add and subtract polynomials, we need to review some definitions presented in Section 3.1. The addends of an algebraic expression are called the terms of the expression. For example, 3x + 5 (Two terms), 7y 2 + ( 6y) + 4 (Three terms). A term that is only a number has a special name. It is called a constant term, or simply a constant. The number factor of a variable is called the numerical coeffi cient, or simply coeffi cient. (RCC) 10.1 July / 15

7 Preliminaries: Example 0: (Finding the terms of an algebraic expression) Identify the term and the coeffi cient of : 4x 2 5x + 3x + 2x 2 5 Term Coeffi cient Like Terms (or Similar Terms) are terms that contain the same variables (if any) raised to the same powers. Like Terms Unlike Terms (RCC) 10.1 July / 15

8 Adding Polynomials Some terms are also monomials. A term is a monomial if the term contains only whole-number exponents and no variable in the denominator. Monomials Not Monomials (RCC) 10.1 July / 15

9 Adding Polynomials Definition: Polynomials A polynomial is a monomial or a combination of sums and/or differences of monomials. Examples of polynomials : (RCC) 10.1 July / 15

10 Adding Polynomials Polynomials with just one term are called monomials. Polynomials Monomials Binomials Trinomials More Than Three Terms (RCC) 10.1 July / 15

11 Adding Polynomials Polynomials with just one term are called monomials. Polynomials with just two terms are called binomials. Polynomials Monomials Binomials Trinomials More Than Three Terms (RCC) 10.1 July / 15

12 Adding Polynomials Polynomials with just one term are called monomials. Polynomials with just two terms are called binomials. Polynomials with just three terms are called trinomials. Polynomials Monomials Binomials Trinomials More Than Three Terms (RCC) 10.1 July / 15

13 Adding Polynomials Adding Polynomials: To add polynomials, combine like terms. Example 1: (Adding polynomials) Add: a) (3y + 7) + ( 9y 14) b) ( x 2 4x 3 ) + ( 5x 2 6x ) (RCC) 10.1 July / 15

14 Adding Polynomials c) ( m 2 4.2m + 11 ) + ( 9m 2 1.9m ) d) ( x 2 x ) + ( 8x 2 x 6.7 ) (RCC) 10.1 July / 15

15 Subtracting Polynomials To subtract one polynomial from another, recall how we subtract numbers. Recall from Section 2.3 that to subtract a number, we add its opposite: a b = a + ( b). To subtract a polynomial, we also add its opposite. Let s practice simplifying the opposite of a polynomial. Example 2: (Finding the opposite of a polynomial) Simplify: a) ( 3y 2 + y 2 ) b) ( 3m 2 + m 7 ) (RCC) 10.1 July / 15

16 Subtracting Polynomials This means that the opposite of a polynomial can be found by changing the signs of the terms of the polynomial. This leads to the following. Subtracting Polynomials: To subtract polynomials, change the signs of the terms of the polynomial being subtracted, then add. (RCC) 10.1 July / 15

17 Subtracting Polynomials Example 3: (Subtracting polynomials) a) (9b + 8) (11b 20) b) ( 11x 2 + 7x + 2 ) ( 15x 2 + 4x ) (RCC) 10.1 July / 15

18 Subtracting Polynomials c) ( 7y 2 + y 4 ) ( 3y 2 + 5y ) d) ( 3m 2 12m ) ( 4m m + 17 ) (RCC) 10.1 July / 15

19 Evaluating Polynomials Example 4: (Evaluating polynomials) Find the value of the polynomial 2y 3 + y 2 6 when y = 3. (RCC) 10.1 July / 15

20 Evaluating Polynomials Example 5: (Evaluating polynomials) An object is dropped from the top of a 530-foot cliff. Its height in feet at time t seconds is given by the polynomial 16t Find the height of the object when t = 4 seconds. (RCC) 10.1 July / 15