Reminder n Like terms have The same variable

Reminder! n Like terms have: ¨ The same variable AND ¨ The same exponent n When combining like terms, add or subtract the numbers, but DO NOT touch the exponents! ¨ Examples: ¨ 6 a + a = 7 a ¨ 3 x 2 + 5 x 2 = 8 x 2 ¨ 6 y 2 – y 2 = 5 y 2

n A term is either a single number or a variable, or numbers and variables multiplied together. n 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) n n n

Polynomials in Standard Form The standard form of a polynomial is written with the terms in order from greatest degree to least degree. Ex 1: 3 x 2 – 4 x 5 – 7 x Answer: -4 x 5 + 3 x 2 – 7 x The leading coefficient is -4 n Ex 2: 5 y + 9 – 2 y 4 – 6 y 3 Answer: -2 y 4 – 6 y 3 + 5 y + 9 The leading coefficient is -2

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

Fri, 3/16 SWBAT…add & subtract polynomials and multiply a monomial by a polynomial Agenda 1. 2. 3. 4. 5. WU (8 min) Adding polynomials review from yesterday (2 min) Subtracting polynomials (15 min) Multiplying a monomial by a polynomial (10 min) Solving equations with polynomials (10 min) HW#5: Polynomials and HW#6: Multiplying two binomials Quiz Monday on HW#5 and HW#6 Test is on Wednesday!

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

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

Multiplying a Monomial with a Polynomial Find the product & arrange in standard form: 4. ) 9 x²(6 x 4 – 2 x³ + 3 x² – x) Answer: 54 x 6 – 18 x 5 + 27 x 4 – 9 x 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. ) 2 k(-3 k + 4) + 6(k 2 + 10) = k(4 k + 8) – 2 k(2 k + 5) k = -6 7. ) 9 c(c – 11) + 10(5 c – 3) = 3 c(c + 5) + c(6 c – 3) – 30 c=0