1. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.1 – Slide 1

2. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.1 – Slide 2 Exponents and Polynomials Chapter 5

3. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.1 – Slide 3 5.1 Adding and Subtracting Polynomials

4. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.1 – Slide 4 5.1 Adding and Subtracting Polynomials Objectives 1.Review combining like terms. 2.Know the vocabulary for polynomials. 3.Evaluate polynomials. 4.Add polynomials. 5.Subtract polynomials. 6.Add and subtract polynomials with more than one variable.

5. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.1 – Slide 5 5.1 Adding and Subtracting Polynomials Review Combining Like Terms (a)– 3 x + 7 x 55 = (– 3 + 7) x 5 = 4 x 5 = (2 + 5 – 1) n 3 = 6 n 3 (b)2 n + 5 n – n 333 Distributive property Example 1 Simplify each expression by adding like terms. Distributive property

6. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.1 – Slide 6 5.1 Adding and Subtracting Polynomials Review Combining Like Terms (c)4 g h – 9 g h + 2 g h 777444 = (4 – 9 + 2) g h 74 = – 3 g h 74 Example 1 (concluded) Simplify each expression by adding like terms. Distributive property

7. Example 2 Simplify each polynomial if possible. Then give the degree and tell whether the polynomial is a monomial, a binomial, a trinomial, or none of these. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.1 – Slide 7 5.1 Adding and Subtracting Polynomials Knowing the Vocabulary for Polynomials (a)2 t + 7 4 The polynomial cannot be simplified. The degree is 4. The polynomial is a binomial. The polynomial can be simplified. The degree is 2. The simplified polynomial is a monomial. (b)3 e + 5 e – 9 e 222 = – e 2 Two terms. One term.

8. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.1 – Slide 8 5.1 Adding and Subtracting Polynomials Evaluating a Polynomial Substitute h = –3. Example (a) Find the value of 5h 4 – 3h 2 + 4h + 7 when h = – 3. Apply the exponents. Multiply. Add and subtract.

9. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.1 – Slide 9 5.1 Adding and Subtracting Polynomials Evaluating a Polynomial Substitute h = 2. Example (concluded) (b) Find the value of 5h 4 – 3h 2 + 4h + 7 when h = 2. Apply the exponents. Multiply. Add and subtract.

10. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.1 – Slide 10 5.1 Adding and Subtracting Polynomials Evaluating a Polynomial CAUTION Use parentheses around the numbers that are substituted for the variable in Example 3, particularly when substituting a negative number for a variable that is raised to a power. Otherwise, a sign error may result.

11. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.1 – Slide 11 5.1 Adding and Subtracting Polynomials Adding Polynomials To add two polynomials, add like terms.

12. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.1 – Slide 12 5.1 Adding and Subtracting Polynomials Adding Polynomials Example 4 8y – 7y – y + 3 32 6y + 2y – 4y + 1 32 + 4– 5y 14y 32 – 5y Write like terms in columns. Now add, column by column.

13. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.1 – Slide 13 5.1 Adding and Subtracting Polynomials Adding Polynomials + 12 – 7n 7n 7n 32 + n Write like terms in columns. Now add, column by column. n – 9n + 12 2 7n 7n 3 + 2n Example 4 (concluded)

14. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.1 – Slide 14 5.1 Adding and Subtracting Polynomials Adding Polynomials – 3n 4 – 15n 3 + 6= Example 5 ( 2n – 7n – 4 ) + ( – 5n – 8n + 10 ) 43 4 3

15. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.1 – Slide 15 5.1 Adding and Subtracting Polynomials Adding Polynomials 7p7p 3 – 4p – 5= 3 Example 5 (concluded) ( 7p – 9p – 4 ) + ( 5p – 1 )

16. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.1 – Slide 16 5.1 Adding and Subtracting Polynomials Subtracting Polynomials To subtract two polynomials, change all the signs of the second polynomial and add the result to the first polynomial.

17. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.1 – Slide 17 5.1 Adding and Subtracting Polynomials Subtracting Polynomials ( 3x – 5 ) – ( 6x – 4 ) Change the signs in the second polynomial and add. – 3x= – 1 Example 6 = ( 3x – 5 ) + ( – 6x + 4 )

18. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.1 – Slide 18 5.1 Adding and Subtracting Polynomials Subtracting Polynomials Change the signs in the second polynomial and add. = ( 7y + 8 ) – ( y + 4y – 2 ) 332 6y6y 3 – 4y 2 + 10 Write the problem. Example 6 (concluded) = ( 7y + 8 ) + ( – y – 4y + 2 ) 33 2

19. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.1 – Slide 19 5.1 Adding and Subtracting Polynomials Subtracting Polynomials Arrange like terms in columns.. 4g + 6g – g – 5 43 – 6g + 2g – 4g + 3 43 6g – 2g + 4g – 3 43 4g + 6g – g – 5 43 Change all signs in the second row, then add. + 4g 3 + 3g– 8 10g 4 Example 7

20. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.1 – Slide 20 5.1 Adding and Subtracting Polynomials Subtracting Polynomials Example 8 Perform the indicated operations to simplify the expression. Rewrite, changing the subtraction to adding the opposite. Combine like terms. 5 = – 8m 2 + 15m ( 2 – 3m + 5m ) + ( – 6 – 4m + 7m ) + ( 9 – m + 3m ) 2 22 = ( 2 – 3m + 5m ) – ( 6 + 4m – 7m ) + ( 9 – m + 3m ). 22 2

21. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.1 – Slide 21 5.1 Adding and Subtracting Polynomials Adding and Subtracting Multivariable Polynomials Example 9 (a) Add or subtract as indicated. = 9c+ 7cd– 3d ( 6c – 2cd + d ) + ( 3c + 9cd – 4d )

22. Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.1 – Slide 22 5.1 Adding and Subtracting Polynomials Adding and Subtracting Multivariable Polynomials Example 9 (concluded) (b) Add or subtract as indicated. – ab ( 2a b – 4ab + b ) – ( 5a b – 3ab + 7b ) 22 2 2 2 22 2 = – 3a b 2 – 6b 2 = 2a b – 4ab + b – 5a b + 3ab – 7b