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Wed, 3/23 SWBAT…add and subtract polynomials Agenda 1. Adding & subtracting polynomials (10 min) 2. Multiplying a monomial by a polynomial (10 min) Warm-Up: 1. What do you need to combine like terms? 2. x + x = 3. x 2 + x 2 = 4. 3x 2 + 5x 2 = 5. -4x – 3x = 6. 3x 3 + 5x 3 = HW#5: Adding & Subtracting Polynomials

A term is either a single number or a variable, or numbers and variables multiplied together. A monomial is one term A binomial is the sum or difference of two monomials A trinomial is the sum or difference of three monomials A polynomial is a monomial or the sum or difference of monomials (not division)

Polynomials in Standard Form The standard form of a polynomial is written with the terms in order from greatest degree to least degree. Ex1: 3x 2 – 4x 5 – 7x Answer: -4x 5 + 3x 2 – 7x The leading coefficient is 4 Ex2: 5y + 9 – 2y 4 – 6y 3 Answer: -2y 4 – 6y 3 + 5y + 9 The leading coefficient is -2

Reminder! Like terms have:  The same variable AND  The same exponent When combining like terms, add or subtract the numbers, but DO NOT touch the exponents!  For example, 6a + 4a = 10a  For example, 6c 2 – 4c 2 = 2c 2

Adding polynomials Find each sum and arrange in standard form: 1. (3x 2 + 5) + (5x 2 + 7) 2. (2x 2 – 4x + 3) + (x 2 – 3x + 1)

Adding polynomials Find each sum and arrange in standard form: 1. (3x 2 + 5) + (5x 2 + 7) = 8x 2 + 12 2. (2x 2 – 4x + 3) + (x 2 – 3x + 1) = 3x 2 – 7x + 4

Subtracting polynomials Find each difference and arrange in standard form: 1.(6c 2 + 5c – 3) – (4c 2 + c) 2.(5y 4 + 3y 3 – 10y + 3) – (5y 3 + y 2 + 7)

Mon, 3/12 SWBAT…add & subtract polynomials and multiply a monomial by a polynomial Agenda 1. WU (15 min) 2. Work on HW#5 (15 min) 3. Exit slip: (5 min) Warm-Up: 1.) For the polynomial: x 2 + 1, name the: a.) Terms b.) Degree c.) Function name Find the difference & arrange in standard form: 2.) (4y 4 + 3y 3 + 11y + 3) – (7y 3 + 4y 2 + 2) 3.) (8x 2 + 7x – 5) – (3x 2 – 4x) – (-6x 3 – 5x 2 + 3) HW#5: Polynomials

Adding and Subtracting Polynomials: Find the difference & arrange in standard form: 2.) (4y 4 + 3y 3 + 11y + 3) – (7y 3 + 4y 2 + 2) 4y 4 + 3y 3 + 11y + 3 – 7y 3 – 4y 2 – 2 Answer: 4y 4 – 4y 3 – 4y 2 + 11y + 1 3.) (8x 2 + 7x – 5) – (3x 2 – 4x) – (-6x 3 – 5x 2 + 3) Answer: 6x 3 + 10x 2 + 4y 2 + 11x – 8

Properties of Polynomials: Use the polynomial 3x – x 2 + 1 to answer questions a – g: a. How many terms does the polynomial have? b. List the three terms: c. What is the degree of the polynomial? d. Write the polynomial in standard form: e. What is the leading coefficient? f. What is the name of the function? g. What is the graph called?

Multiplying a Monomial with a Polynomial: Find the product & arrange in standard form: 4.) 9x²(6x 4 – 2x³ + 3x² – x) Answer: 54x 6 –18x 5 + 27x 4 – 9x 3 5.) -xy(x 6 – x 3 – xy) Answer: -x 7 y + x 4 y + x 2 y 2

Solving Equations with Polynomials: Solve each equation: 6.) 2k(-3k + 4) + 6(k 2 + 10) = k(4k + 8) – 2k(2k + 5) k = -6 7.) 9c(c – 11) + 10(5c – 3) = 3c(c + 5) + c(6c – 3) – 30 c = 0

Work on HW#5

Exit Slip: Complete on a ½ sheet 1. Simplify: -x(x 3 – x 2 ) 2. Simplify: 9b²(2b³ – 3b² + b) 3. Solve: 7(2w 2 + 8w – 3) + 13 = 2(7w 2 + 6w + 7)

HW#5 Answers 1.) 8x 2 + 12 2.) 3x 2 – 7x + 4 3.) 2c 2 + c – 3 4.) 3x 2 + 3x – 20 5.) -2y 3 – y 2 – 11y + 1 6.) 3n 2 – n – 4

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