I CAN classify polynomials by degree and by the number of terms.

Transcription

1 13-1 Polynomials I CAN classify polynomials by degree and by the number of terms.

2 13-1 Polynomials Insert Lesson Title Here Vocabulary monomial polynomial binomial trinomial degree of a polynomial

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4 13-1 Polynomials The simplest type of polynomial is called a monomial. A monomial is a number or a product of numbers and variables with exponents that are whole numbers. Monomials 2n, x 3, 4a 4 b 3, 7 Not monomials p 2.4, 2 x 5, x, g 2

5 13-1 Polynomials Additional Example 1: Identifying Monomials Determine whether each expression is a monomial. A. 2 x 3 y 4 B. 3x 3 y

6 13-1 Polynomials Try This: Example 1 Determine whether each expression is a monomial. A. 2w p 3 y 8 B. 9t 3.2 z

7 13-1 Polynomials A polynomial is one monomial or the sum or difference of monomials. Polynomials can be classified by the number of terms. A monomial has 1 term, a binomial has 2 term, and a trinomial has 3 terms.

8 13-1 Polynomials Additional Example 2: Classifying Polynomials by the Number of Terms Classify each expression as a monomial, a binomial, a trinomial, or not a polynomial. A. xy 2 B. 2x 2 4y 2 C. 3x x 2 4 D. a 2 + b 2

9 13-1 Polynomials Try This: Example 2 Classify each expression as a monomial, a binomial, a trinomial, or not a polynomial. A. 4x 2 + 7z 4 B. 1.3x 2.5 4y C. 6.3x 2 D. c 99 + p 3

10 13-1 Polynomials A polynomial can also be classified by its degree. The degree of a polynomial is the degree of the term with the greatest degree. 4x 2 + 2x 5 + x + 5 Degree 2 Degree 5 Degree 1 Degree 0 Degree 5

11 13-1 Polynomials Additional Example 3A & 3B: Classifying Polynomials by Their Degrees Find the degree of each polynomial. A. x + 4 B. 5x 2x 2 + 6

12 13-1 Polynomials Additional Example 3C: Classifying Polynomials by Their Degrees Find the degree of the polynomial. C. 3x 4 + 8x 5 4x 6

13 13-1 Polynomials Try This: Example 3A & 3B Find the degree of each polynomial. A. y B. x + 4x 4 + 2y

14 13-1 Polynomials Try This: Example 3C Find the degree of each polynomial. C. 6x 4 9x 8 + x 2 6x 4 9x 8 + x 2 Degree 4 Degree 8 Degree 2 The degree of 6x 4 9x 8 + x 2 is 8.

15 13-2 Simplifying Polynomials I CAN simplify polynomials.

16 13-2 Simplifying Polynomials Additional Example 1A & 1B: Identifying Like Terms Identify the like terms in each polynomial. A. 5x 3 + y y 2 + 4x 3 B. 3a 3 b 2 + 3a 2 b 3 + 2a 3 b 2 - a 3 b 2

17 13-2 Simplifying Polynomials Additional Example 1C: Identifying Like Terms Identify the like terms in the polynomial. C. 7p 3 q 2 + 7p 2 q 3 + 7pq 2

18 13-2 Simplifying Polynomials Try This: Example 1A & 1B Identify the like terms in each polynomial. A. 4y 4 + y y 2 + 2y 4 B. 7n 4 r 2 + 3a 2 b 3 + 5n 4 r 2 + n 4 r 2

19 13-2 Simplifying Polynomials Try This: Example 1C Identify the like terms in the polynomial. C. 9m 3 n 2 + 7m 2 n 3 + pq 2

20 13-2 Simplifying Polynomials To simplify a polynomial, combine like terms. It may be easier to arrange the terms in descending order (highest degree to lowest degree) before combining like terms.

21 13-2 Simplifying Polynomials Simplify. Additional Example 2A: Simplifying Polynomials by Combining Like Terms A. 4x 2 + 2x x + 9

22 13-2 Simplifying Polynomials Simplify. Additional Example 2B: Simplifying Polynomials by Combining Like Terms B. 3n 5 m 4 6n 3 m + n 5 m 4 8n 3 m

23 13-2 Simplifying Polynomials Simplify. Try This: Example 2A A. 2x 3 + 5x x + 9

24 13-2 Simplifying Polynomials Try This: Example 2B Simplify. B. 2n 5 p 4 7n 6 p + n 5 p 4 9n 6 p

25 13-2 Simplifying Polynomials Sometimes you may need to use the Distributive Property to simplify a polynomial.

26 13-2 Simplifying Polynomials Additional Example 3A: Simplifying Polynomials by Using the Distributive Property Simplify. A. 3(x 3 + 5x 2 )

27 13-2 Simplifying Polynomials Additional Example 3B: Simplifying Polynomials by Using the Distributive Property Simplify. B. 4(3m 3 n + 7m 2 n) + m 2 n

28 13-2 Simplifying Polynomials Try This: Example 3A Simplify. A. 2(x 3 + 5x 2 )

29 13-2 Simplifying Polynomials Simplify. Try This: Example 3B B. 2(6m 3 p + 8m 2 p) + m 2 p

30 13-3 Adding Polynomials I CAN add polynomials.

31 13-3 Adding Polynomials Add. Additional Example 1A: Adding Polynomials Horizontally A. (5x 3 + x 2 + 2) + (4x 3 + 6x 2 )

32 13-3 Adding Polynomials Add. Additional Example 1B: Adding Polynomials Horizontally B. (6x 3 + 8y 2 + 5xy) + (4xy 2y 2 )

33 13-3 Adding Polynomials Add. Additional Example 1C: Adding Polynomials Horizontally C. (3x 2 y 5x) + (4x + 7) + 6x 2 y

34 13-3 Adding Polynomials Try This: Example 1A Add. A. (3y 4 + y 2 + 6) + (5y 4 + 2y 2 )

35 13-3 Adding Polynomials Try This: Example 1B Add. B. (9x 3 + 6p 2 + 3xy) + (8xy 3p 2 )

36 13-3 Adding Polynomials Try This: Example 1C Add. C. (3z 2 w 5x) + (2x + 8) + 6z 2 w

37 13-3 Adding Polynomials You can also add polynomials in a vertical format. Write the second polynomial below the first one, lining up the like terms. If the terms are rearranged, remember to keep the correct sign with each term.

38 13-3 Adding Polynomials Add. Additional Example 2A: Adding Polynomials Vertically A. (4x 2 + 2x + 11) + (2x 2 + 6x + 9)

39 13-3 Adding Polynomials Add. Additional Example 2B & 2C: Adding Polynomials Vertically B. (3mn 2 6m + 6n) + (5mn 2 + 2m 6n) C. ( x 2 y 2 + 5x 2 ) + ( 2y 2 + 2) + (x 2 + 8)

40 13-3 Adding Polynomials Try This: Example 2A Add. A. (6x 2 + 6x + 13) + (3x 2 + 2x + 4)

41 13-3 Adding Polynomials Add. Try This: Example 2B & 2C B. (4mn 2 + 6m + 2n) + (2mn 2 2m 2n) C. (x 2 y 2 5x 2 ) + (2y 2 2) + (x 2 )

42 13-3 Adding Insert Lesson Polynomials Title Here Add. Lesson Quiz: Part 1 1. (2m 2 3m + 7) + (7m 2 1) 9m 2 3m (yz 2 + 5yz + 7) + (2yz 2 yz) 3yz 2 + 4yz (2xy 2 + 2x 6) + (5xy 2 + 3y + 8) 7xy 2 + 2x + 3y + 2

43 13-4 Subtracting Polynomials I CAN subtract polynomials.

44 13-4 Subtracting Polynomials To subtract a polynomial, add its opposite.

45 13-4 Subtracting Polynomials Additional Example 2A: Subtracting Polynomials Horizontally Subtract. A. (5x 2 + 2x 3) (3x 2 + 8x 4)

46 13-4 Subtracting Polynomials Additional Example 2B: Subtracting Polynomials Horizontally Subtract. B. (b 2 + 4b 1) (7b 2 b 1)

47 13-4 Insert Subtracting Lesson Polynomials Title Here Subtract. Try This: Example 2A A. (2y 3 + 3y + 5) (4y 3 + 3y + 5)

48 13-4 Insert Subtracting Lesson Polynomials Title Here Subtract. Try This: Example 2B B. (c 3 + 2c 2 + 3) (4c 3 c 2 1)

49 13-4 Subtracting Polynomials Additional Example 3A: Subtracting Polynomials Vertically Subtract. A. (2n 2 4n + 9) (6n 2 7n + 5)

50 13-4 Subtracting Polynomials Additional Example 3B: Subtracting Polynomials Vertically Subtract. B. (10x 2 + 2x 7) (x 2 + 5x + 1)

51 13-4 Subtracting Polynomials Additional Example 3C: Subtracting Polynomials Vertically Subtract. C. (6a 4 3a 2 8) ( 2a 4 + 7)

52 13-4 Insert Subtracting Lesson Polynomials Title Here Subtract. Try This: Example 3A A. (4r 3 + 4r + 6) (6r 3 + 3r + 3)

53 13-4 Insert Subtracting Lesson Polynomials Title Here Subtract. Try This: Example 3B B. (13y 2 2x + 5) (y 2 + 5x 9)

54 13-4 Insert Subtracting Lesson Polynomials Title Here Subtract. Try This: Example 3C C. (5x 2 + 2x + 5) ( 3x 2 7x)

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