3 Add Polynomials Procedure Adding Polynomials To add polynomials, add like terms. We can set up an addition problem vertically or horizontally. Remember that the exponents remain unchanged when we add like terms. EXAMPLE 3 In-Class Example 3 Add t3 4t2 7t 5 and 6t3 t2 3 vertically. Answer: 7t3 5t2 7t 8 Add m3 9m2 5m 4 and 2m3 3m2 1 vertically. Solution Line up like terms in columns and add the terms in the same column. m3 9m2 5m 4 2m3 3m2 1 3m3 6m2 5m 5 YOU TRY 3 Add (6b3 11b2 3b 3) (2b3 6b2 b 8). EXAMPLE 4 In-Class Example 4 Add 9a2 11a 3 and 6a2 9a 5 horizontally. Answer: 15a2 2a 8 Add 10k2 2k 1 and 5k2 7k 9 horizontally. Solution Put the polynomials in parentheses since each contains more than one term. Use the associative and commutative properties to rewrite like terms together. (10k2 2k 1) (5k2 7k 9) (10k2 5k2) (2k 7k) (1 9) 15k2 9k 8 Combine like terms. 4 Subtract Polynomials To subtract two polynomials such as (8x 3) (5x 4), we will be using the distributive property to clear the parentheses in the second polynomial. EXAMPLE 5 In-Class Example 5 Subtract (6c 1) (4c 9) Answer: 2c 10 Subtract (8x 3) (5x 4). Solution (8x 3) (5x 4) (8x 3) 1(5x 4 ) (8x 3) (1)(5x 4 ) Change 1 to (1). (8x 3) (5x 4 ) Distribute. 3x 7 Combine like terms. In Example 5, notice that we changed the sign of each term in the second polynomial and then added it to the fi rst. www.mhhe.com/messersmith SECTION 10.4 Adding and Subtracting Polynomials 793
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