Identify terms and coefficients. Know the vocabulary for polynomials.

1. 5.4 Polynomials Vocabulary 2 1 2 Identify terms and coefficients. Know the vocabulary for polynomials.

2. Identify terms and coefficients. In an expression such as the quantities 4x3, 6x2, 5x, and 8 are called terms. In the first term 4x3, the number 4 is called the coefficient, of x3. In the same way, 6 is the coefficient of x2 in the term 6x2, and 5 is the coefficient of x in the term 5x. The constant term is 8 . Slide 5.4-4

3. Name the coefficient of each term in the expression EXAMPLE 1 Identifying Coefficients Solution: Slide 5.4-5

4. Know the vocabulary for polynomials. A polynomial in x is a term or the sum of a finite number of terms of the form axn, for any real number a and any whole number (no negative, no fraction) n. For example, is a polynomial in x. (The 4 can be written as 4x0.) This polynomial is written in standard form, since the exponents on x decrease from left to right. Polynomial in x By contrast, is not a polynomial in x, since x appears in a denominator. Not a Polynomial A polynomial can be defined using any variable and not justx. In fact, polynomials may have terms with more than one variable. Slide 5.4-10

5. Know the vocabulary for polynomials. (cont’d) The degree of a term is the sum of the exponents on the variables. For example 3x4 has degree 4, while the term 5x (or 5x1) has degree 1, −7 has degree 0 ( since −7 can be written −7x0). The degree of a polynomial is the greatest degree term of the polynomial. For example 3x4 + 5x2 + 6 is of degree 4. Slide 5.4-11

6. and Monomials A polynomial with exactly two terms is called a binomial. (Bi- means “two,” as in bicycle.) Examples are and Binomials A polynomial with exactly three terms is called a trinomial.(Tri-means “three,” as in triangle.) Examples are and Trinomials Know the vocabulary for polynomials. (cont’d) Three types of polynomials are common and given special names. A polynomial with only one term is called a monomial.(Mono-means “one,” as in monorail.) Examples are Slide 5.4-12

7. Know the vocabulary for polynomials. (cont’d)

8. EXAMPLE 3 Classifying Polynomials Write polynomial in standard form, give the degree, and tell whether the polynomial is a monomial, binomial, trinomial. 3x + 5x3 - 4 Solution: 5x3 + 3x – 4 Degree 3 or cubic, trinomial Slide 5.4-13

9. Add like terms. like termshave exactly the same combinations of variables, with the same exponents on the variables. Onlythe coefficients may differ. Examples of like terms We combine, or add, like terms by adding their coefficients. Slide 5.4-7

10. EXAMPLE 2 Adding Like Terms Simplify by adding like terms. Solution: Unlike terms cannot be combined. Unlike terms have different variables or different exponents on the same variables. Slide 5.4-8

11. Add and subtract polynomials. Polynomials may be added, subtracted, multiplied, and divided. Adding Polynomials To add two polynomials, add like terms. Subtracting Polynomials To subtract two polynomials, change all the signs in the second polynomial and add the result to the first polynomial. Slide 5.4-17

12. + + EXAMPLE 5 Adding Polynomials Vertically Add. and and Solution: Slide 5.4-18

13. EXAMPLE 6 Adding Polynomials Horizontally Add. Solution: Slide 5.4-19

14. EXAMPLE 7 Subtracting Polynomials Horizontally Perform the subtractions. from Solution: Slide 5.4-20

15. + EXAMPLE 8 Subtracting Polynomials Vertically Subtract. Solution: Slide 5.4-21

16. EXAMPLE 9 Adding and Subtracting Polynomials with More Than One Variable Subtract. Solution: Slide 5.4-22

17. EXAMPLE 4 Evaluating a Polynomial Find the value of 2y3 + 8y− 6 when y = −1. Solution: Use parentheses around the numbers that are being substituted for the variable, particularly when substituting a negative number for a variable that is raised to a power, or a sign error may result. Slide 5.4-15