1. Add and Subtract Polynomials

2. Lesson Essential Question How do you add and subtract polynomials?

3. Terminology Monomial – a number, a variable, or the product of a number and one or more variables with whole number exponents Degree of a monomial – the sum of the exponents of the variables in the monomial Polynomial – a monomial or a sum of monomials, each called a term of the polynomial Degree of polynomial – the greatest degree of its terms Leading coefficient – when a polynomial is written so that the exponents of a variable decrease from left to right, it is the coefficient of the first term Binomial – a polynomial with two terms Trinomial – a polynomial with three terms

4. Example 1: Rewrite a polynomial Write each of the following so that the exponents decrease from left to right. Identify the degree and leading coefficient of the polynomial. 1) 15x – x 3 + 32) 3b 3 – 4b 4 + b 2 – 2 + b 3) 5y – 2y 2 + 9 – y 3

5. Example 2: Identify and Classify Polynomials Complete the following. ExpressionIs it a polynomial? Classify by degree & number of terms 9 2x 2 + x – 5 6n 4 – 8n n -2 - 3 7bc 3 +4b 4 c 5xy 2 3a -5 x 4 +3x 3 – x 9/m 6a 2 c +5ac 5

6. Example 3: Add Polynomials Find the sum. 1) (2x 3 – 5x 2 + x) + (2x 2 + x 3 – 1) 2) (3x 2 + x – 6) + (x 2 + 4x + 10) 3) (5x 3 + 4x – 2x) + (4x 2 + 3x 3 – 6) 4) (-2x 2 + 3x – x 3 ) + (3x 2 + x 3 – 12)

7. Example 4: Subtract Polynomials Find the difference. 1) (4n 2 + 5) – (-2n 2 + 2n – 4) 2) (4x 2 – 3x + 5) – (3x 2 – x – 8) 3) (4x 2 – 7x) – (5x 2 + 4x – 9) 4) (2c 2 – 8) – (3c 2 – 4c + 1)

8. Example 5: Application Problems During the period 1999 – 2005, the number of hours an individual person watched broadcast television B and cable and satellite television C can be modeled by B = 2.8t 2 – 35t + 879 and C = -5t 2 + 80t + 712 where t is the number of years since 1999. About how many hours did people watch television in 2002?

9. Summary Question How do you add and subtract polynomials?