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

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

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

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

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

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

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.

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 5 + 2.2x 2 4 D. a 2 + b 2

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

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

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

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

13-1 Polynomials Try This: Example 3A & 3B Find the degree of each polynomial. A. y + 9.9 B. x + 4x 4 + 2y

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.

13-2 Simplifying Polynomials I CAN simplify polynomials.

13-2 Simplifying Polynomials Additional Example 1A & 1B: Identifying Like Terms Identify the like terms in each polynomial. A. 5x 3 + y 2 + 2 6y 2 + 4x 3 B. 3a 3 b 2 + 3a 2 b 3 + 2a 3 b 2 - a 3 b 2

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

13-2 Simplifying Polynomials Try This: Example 1A & 1B Identify the like terms in each polynomial. A. 4y 4 + y 2 + 2 8y 2 + 2y 4 B. 7n 4 r 2 + 3a 2 b 3 + 5n 4 r 2 + n 4 r 2

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

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.

13-2 Simplifying Polynomials Simplify. Additional Example 2A: Simplifying Polynomials by Combining Like Terms A. 4x 2 + 2x 2 + 7 6x + 9

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

13-2 Simplifying Polynomials Simplify. Try This: Example 2A A. 2x 3 + 5x 3 + 6 4x + 9

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

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

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

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

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

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

13-3 Adding Polynomials I CAN add polynomials.

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

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

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

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

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

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

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.

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

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)

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

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 )

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

13-4 Subtracting Polynomials I CAN subtract polynomials.

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

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

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

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

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

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

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

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

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

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

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