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

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Presentation transcript:

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

Polynomials? Mono- is a prefix meaning “one” What are 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 Polynomials?

How do we work with 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. Polynomials?

Review – Adding, Subtracting, & Multiplying Adding – Combine Like Terms Subtracting – Add the Opposite Subtracting Polynomials Adding Polynomials (a3 – 2a2) – (3a2 – 4a3) Add the opposite, so… (a3 – 2a2) + (-3a2 + 4a3) Combine like terms… a3 + 4a3 = 5a3 -2a2 + -3a2 = -5a2 5a3 – 5a2 (5p2 -3) + (2p2 – 3p3) Identify like terms and combine them. 5p2 + 2p2 = 7p2 Write in descending order of the exponents. -3p3 + 7p2 -3

Review – Adding, Subtracting, & Multiplying Multiplying – Multiply the Constants, then the Variables – DISTRIBUTE!!! Examples: binomial by a binomial monomials 3. (x + 2) (x + 5) 4. (3x + 10) (2x – 5) 1. 2x2 * 5x3 = 10x5 monomial and a polynomial polynomial by a polynomial 2. 2x2 (3x3 – 4x2 + x – 5) 5. (x + 2) (x2 + 5x + 6) 6x5 – 8x4 + 2x3 – 10x2 6. (x2 – 2x + 1) (x2 + 5x + 6)

Long Division For Polynomials

Divide a Polynomial by a Binomial 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. Ex: (x2 – 10x – 24 ) ÷ (x + 2) (8x4 – 4x2 + x +4) ÷ (2x + 1) (x3 + y3) ÷ (x + y)

You Try 1. (3a4 – 6a3 – 2a2 + a – 6) ÷ (a + 1) 2. (t2 + 3t – 9) ÷ (5 – t ) Hint: reorder the denominator 3. (3x3 – 5x2 + 10x – 3) ÷ (3x + 1)

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

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