Procedure Subtracting Polynomials To subtract two polynomials, change the sign of each term in the second polynomial. Then, add the polynomials. Let’s see how we use this rule to subtract polynomials both horizontally and vertically. Subtract vertically: (6w3 w2 10w 1) (2w3 4w2 9w 5) Solution To subtract vertically, line up like terms in columns. 6w3 w2 10w 1 (2w3 4w2 9w 5) Change the signs in the second polynomial and add the polynomials. 6w3 w2 10w 1 2w3 4w2 9w 5 8w3 3w2 w 6 YOU TRY 4 Subtract (7h2 8h 1) (3h2 h 4) Subtract 6a3 7a 4 from 2a3 3a 9. Solution Be sure to set up the subtraction problem in the correct order. (2a3 3a 9) (6a3 7a 4) Change the signs in the second polynomial, then add the polynomials. (2a3 3a 9) (6a3 7a 4) 8a3 10a 5 YOU TRY 5 Subtract 10w2 w 8 from 6w2 2w 11. ANSWERS TO YOU TRY EXERCISES 1) a) not a polynomial b) polynomial of degree 3 c) not a polynomial Term Degree k3 3 k2 2 3.8k 1 10 0 2) a) 26 b) 46 3) 4b3 17b2 4b 5 4) 10h2 9h 5 5) 16w2 3w 19 EXAMPLE 6 In-Class Example 6 Subtract (5n3 n2 7n 7) (3n3 8n2 2n 4). Answer: 8n3 7n2 5n 11 EXAMPLE 7 In-Class Example 7 Subtract 3m3 10m 1 from 4m3 m 3. Answer: 7m3 9m 2 794 CHAPTER 10 The Rules of Exponents and Polynomials www.mhhe.com/messersmith
messersmith_power_prealgebra_1e_ch4_7_10
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