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


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1 131 Polynomials I CAN classify polynomials by degree and by the number of terms.
2 131 Polynomials Insert Lesson Title Here Vocabulary monomial polynomial binomial trinomial degree of a polynomial
3
4 131 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
5 131 Polynomials Additional Example 1: Identifying Monomials Determine whether each expression is a monomial. A. 2 x 3 y 4 B. 3x 3 y
6 131 Polynomials Try This: Example 1 Determine whether each expression is a monomial. A. 2w p 3 y 8 B. 9t 3.2 z
7 131 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.
8 131 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
9 131 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
10 131 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
11 131 Polynomials Additional Example 3A & 3B: Classifying Polynomials by Their Degrees Find the degree of each polynomial. A. x + 4 B. 5x 2x 2 + 6
12 131 Polynomials Additional Example 3C: Classifying Polynomials by Their Degrees Find the degree of the polynomial. C. 3x 4 + 8x 5 4x 6
13 131 Polynomials Try This: Example 3A & 3B Find the degree of each polynomial. A. y B. x + 4x 4 + 2y
14 131 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.
15 132 Simplifying Polynomials I CAN simplify polynomials.
16 132 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
17 132 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
18 132 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
19 132 Simplifying Polynomials Try This: Example 1C Identify the like terms in the polynomial. C. 9m 3 n 2 + 7m 2 n 3 + pq 2
20 132 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.
21 132 Simplifying Polynomials Simplify. Additional Example 2A: Simplifying Polynomials by Combining Like Terms A. 4x 2 + 2x x + 9
22 132 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
23 132 Simplifying Polynomials Simplify. Try This: Example 2A A. 2x 3 + 5x x + 9
24 132 Simplifying Polynomials Try This: Example 2B Simplify. B. 2n 5 p 4 7n 6 p + n 5 p 4 9n 6 p
25 132 Simplifying Polynomials Sometimes you may need to use the Distributive Property to simplify a polynomial.
26 132 Simplifying Polynomials Additional Example 3A: Simplifying Polynomials by Using the Distributive Property Simplify. A. 3(x 3 + 5x 2 )
27 132 Simplifying Polynomials Additional Example 3B: Simplifying Polynomials by Using the Distributive Property Simplify. B. 4(3m 3 n + 7m 2 n) + m 2 n
28 132 Simplifying Polynomials Try This: Example 3A Simplify. A. 2(x 3 + 5x 2 )
29 132 Simplifying Polynomials Simplify. Try This: Example 3B B. 2(6m 3 p + 8m 2 p) + m 2 p
30 133 Adding Polynomials I CAN add polynomials.
31 133 Adding Polynomials Add. Additional Example 1A: Adding Polynomials Horizontally A. (5x 3 + x 2 + 2) + (4x 3 + 6x 2 )
32 133 Adding Polynomials Add. Additional Example 1B: Adding Polynomials Horizontally B. (6x 3 + 8y 2 + 5xy) + (4xy 2y 2 )
33 133 Adding Polynomials Add. Additional Example 1C: Adding Polynomials Horizontally C. (3x 2 y 5x) + (4x + 7) + 6x 2 y
34 133 Adding Polynomials Try This: Example 1A Add. A. (3y 4 + y 2 + 6) + (5y 4 + 2y 2 )
35 133 Adding Polynomials Try This: Example 1B Add. B. (9x 3 + 6p 2 + 3xy) + (8xy 3p 2 )
36 133 Adding Polynomials Try This: Example 1C Add. C. (3z 2 w 5x) + (2x + 8) + 6z 2 w
37 133 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.
38 133 Adding Polynomials Add. Additional Example 2A: Adding Polynomials Vertically A. (4x 2 + 2x + 11) + (2x 2 + 6x + 9)
39 133 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)
40 133 Adding Polynomials Try This: Example 2A Add. A. (6x 2 + 6x + 13) + (3x 2 + 2x + 4)
41 133 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 )
42 133 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
43 134 Subtracting Polynomials I CAN subtract polynomials.
44 134 Subtracting Polynomials To subtract a polynomial, add its opposite.
45 134 Subtracting Polynomials Additional Example 2A: Subtracting Polynomials Horizontally Subtract. A. (5x 2 + 2x 3) (3x 2 + 8x 4)
46 134 Subtracting Polynomials Additional Example 2B: Subtracting Polynomials Horizontally Subtract. B. (b 2 + 4b 1) (7b 2 b 1)
47 134 Insert Subtracting Lesson Polynomials Title Here Subtract. Try This: Example 2A A. (2y 3 + 3y + 5) (4y 3 + 3y + 5)
48 134 Insert Subtracting Lesson Polynomials Title Here Subtract. Try This: Example 2B B. (c 3 + 2c 2 + 3) (4c 3 c 2 1)
49 134 Subtracting Polynomials Additional Example 3A: Subtracting Polynomials Vertically Subtract. A. (2n 2 4n + 9) (6n 2 7n + 5)
50 134 Subtracting Polynomials Additional Example 3B: Subtracting Polynomials Vertically Subtract. B. (10x 2 + 2x 7) (x 2 + 5x + 1)
51 134 Subtracting Polynomials Additional Example 3C: Subtracting Polynomials Vertically Subtract. C. (6a 4 3a 2 8) ( 2a 4 + 7)
52 134 Insert Subtracting Lesson Polynomials Title Here Subtract. Try This: Example 3A A. (4r 3 + 4r + 6) (6r 3 + 3r + 3)
53 134 Insert Subtracting Lesson Polynomials Title Here Subtract. Try This: Example 3B B. (13y 2 2x + 5) (y 2 + 5x 9)
54 134 Insert Subtracting Lesson Polynomials Title Here Subtract. Try This: Example 3C C. (5x 2 + 2x + 5) ( 3x 2 7x)
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