1. EXAMPLE 1
Rewrite a polynomial
Write 15x – x3 + 3 so that the exponents decrease from left to right. Identify the degree and leading coefficient of the polynomial.
SOLUTION
Consider the degree of each of the polynomial’s terms.
15x – x3 + 3
The polynomial can be written as – x The greatest degree is 3, so the degree of the polynomial is 3, and the leading coefficient is –1.

2. Identify and classify polynomials
EXAMPLE 2
Identify and classify polynomials
Tell whether is a polynomial. If it is a polynomial, find its degree and classify it by the number of its terms. Otherwise, tell why it is not a polynomial.
5th degree binomial
Yes
7bc3 + 4b4c
No; variable exponent
n– 2 – 3
6n4 – 8n
2nd degree trinomial
2x2 + x – 5
0 degree monomial 9
Classify by degree and number of terms
Is it a polynomial?
Expression a. b. c. d. e.

3. EXAMPLE 3
Add polynomials
Find the sum.
a. (2x3 – 5x2 + x) + (2x2 + x3 – 1)
b. (3x2 + x – 6) + (x2 + 4x + 10)

4. EXAMPLE 3
Add polynomials
SOLUTION
a. Vertical format: Align like terms in vertical columns.
(2x3 – 5x2 + x)
+ x3 + 2x – 1
3x3 – 3x2 + x – 1
b. Horizontal format: Group like terms and simplify.
(3x2 + x – 6) + (x2 + 4x + 10) =
(3x2 + x2) + (x + 4x) + (– )
= 4x2 + 5x + 4

5. EXAMPLE 1
GUIDED PRACTICE
Rewrite a polynomial
for Examples 1,2, and 3
Write 5y – 2y2 + 9 so that the exponents decrease from left to right. Identify the degree and leading coefficient of the polynomial. 1.
– 2y2 +5y + 9 Degree: 2, Leading Coefficient: –2
ANSWER
Tell whether y3 – 4y + 3 is a polynomial. If it is a polynomial, find its degree and classify it by the number of its terms. Otherwise, tell why it is not a polynomial. 2.
ANSWER
polynomial Degree: 3, trinomial

6. EXAMPLE 3
GUIDED PRACTICE
Add polynomials
for Examples 1,2, and 3
for Example
Find the sum. 3.
(5x3 + 4x – 2x) + (4x2 +3x3 – 6)
= 8x3 + 4x2 + 2x – 6
ANSWER