Bell Ringer 3 6 19 In elementary school

Bell Ringer 3 -6 -19 §In elementary school, you learned long division. Describe, in detail, how to divide 230 by 4 without a calculator.

Dividing Polynomials Wednesday, March 6, 2019

What are Polynomials? §Mono- is a prefix meaning “one” §Bi- is a prefix meaning “two” §Tri- is a prefix meaning “three” §Poly- is a prefix meaning “many” §-nomial is a suffix meaning “terms” §Polynomial = Many Terms

How do we work with Polynomials? § We can perform operations with polynomials (addition, subtraction, multiplication, and division). § When we write polynomials, the standard is to write in descending order of the exponents. § The degree of a polynomial is the highest exponent or sum of the exponents if there are multiple variables in the same term.

Review – Adding, Subtracting, & Multiplying §Adding – Combine Like Terms §Subtracting – Add the Opposite Adding Polynomials § (5 p 2 -3) + (2 p 2 – 3 p 3) § Identify like terms and combine them. 5 p 2 + 2 p 2 = 7 p 2 § Write in descending order of the exponents. § -3 p 3 + 7 p 2 -3 Subtracting Polynomials § (a 3 – 2 a 2) – (3 a 2 – 4 a 3) § Add the opposite, so… § (a 3 – 2 a 2) + (-3 a 2 + 4 a 3) § Combine like terms… a 3 + 4 a 3 = 5 a 3 -2 a 2 + -3 a 2 = -5 a 2 § 5 a 3 – 5 a 2

Review – Adding, Subtracting, & Multiplying §Multiplying – Multiply the Constants, then the Variables – DISTRIBUTE!!! §Examples: binomial by a binomial 3. (x + 2) (x + 5) monomials 4. (3 x + 10) (2 x – 5) 1. 2 x 2 * 5 x 3 = 10 x 5 monomial and a polynomial by a polynomial 2. 2 x 2 (3 x 3 – 4 x 2 + x – 5) 5. (x + 2) (x 2 + 5 x + 6) 6 x 5 – 8 x 4 + 2 x 3 – 10 x 2 6. (x 2 – 2 x + 1) (x 2 + 5 x + 6)

Long Division For Polynomials

Divide a Polynomial by a Binomial Ex: 1. (x 2 – 10 x – 24 ) ÷ (x + 2) 2. (8 x 4 – 4 x 2 + x +4) ÷ (2 x + 1) 3. (x 3 + y 3) ÷ (x + y) §Just like in elementary school… §Divide §Multiply §Subtract Add the Opposite §Bring Down §If there is a remainder… write it as a fraction. §Like with decimals, you may need a placeholder.

You Try § 1. (3 a 4 – 6 a 3 – 2 a 2 + a – 6) ÷ (a + 1) 2 § 2. (t + 3 t – 9) ÷ (5 – t ) Hint: reorder the denominator § 3. (3 x 3 – 5 x 2 + 10 x – 3) ÷ (3 x + 1)

Polynomial Division Worksheet Classwork (1 -10) Homework (11 -20)

Exit Ticket What are the 4 steps for Polynomial Long Division?