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

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. Identifying Coefficients
EXAMPLE 1
Identifying Coefficients
Name the coefficient of each term in the expression
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 just x. In fact, polynomials may have terms with more than one variable.
Slide

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

6. 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
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
Slide

7. Know the vocabulary for polynomials. (cont’d)
Degree
Name
Example
Constant 5 1
Linear
2x + 4 2
Quadratic
4x2 – 7x + 2 3
Cubic
x3 – 2x2 – 2x + 1 4
Quartic
-8x4 – 7x2 + 3x - 4
Quintic
3x5 – 5x4 + 2x3 – 4x2 +10x – 9
Number of Terms
Name
Example 1
Monomial
3x2 2
Binomial
5x + 4x3 3
Trinomial
3x + 4x3 - 7
More than 3
Polynomial
5x5 + 4x4 - 2x3 + 8x2 - x - 1

8. Classifying Polynomials
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

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

10. Simplify by adding like terms.
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

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

13. Adding Polynomials Horizontally
EXAMPLE 6
Adding Polynomials Horizontally
Add.
Solution:
Slide

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

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

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

17. Evaluating a Polynomial
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