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 – x3 +15 + 3. The greatest degree is 3, so the degree of the polynomial is 3, and the leading coefficient is –1.

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.

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

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

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

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