Remainder and Factor Theorem

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Presentation transcript:

Remainder and Factor Theorem Chapter 2.5

Synthetic Division Synthetic division is a method used to divide any polynomial by a divisor in the form 𝑥−𝑘

Evaluate a function using synthetic substitution 1. Divide 𝑓 𝑥 = 2𝑥 3 + 𝑥 2 −8𝑥+5 by 𝑥 +3

Evaluate a function using synthetic substitution 2. Divide 𝑓 𝑥 = 𝑥 2 +3𝑥−6 by 𝑥+5

Evaluate a function using synthetic substitution 3. Divide 𝑓 𝑥 = 𝑥 2 +4 by 𝑥−2

Evaluate a function using synthetic substitution 4. Divide 𝑓 𝑥 = 2𝑥 3 + 9𝑥 2 +14𝑥+5 by 𝑥−3

Evaluate a function using synthetic substitution 5. Divide 𝑓 𝑥 = 𝑥 2 +2𝑥−11 by 𝑥+2

Factor a Polynomial completely given a factor. 1. 𝑓 𝑥 = 3𝑥 3 −4 𝑥 2 −𝑥−1;𝑥+2

Factor a Polynomial completely given a factor. 2. 𝑓 𝑥 = 2𝑥 3 −11 𝑥 2 +3𝑥+36;𝑥−3

Factor a Polynomial completely given a factor. 3. 𝑓 𝑥 = 𝑥 3 − 𝑥 2 −21𝑥+45;𝑥+5

Factor a Polynomial completely given a factor. 4. 𝑓 𝑥 = 4𝑥 3 − 4𝑥 2 −9𝑥+9;𝑥−1

Given a zero of the function, find the other zeroes 1. 𝑓 𝑥 = 𝑥 3 −2 𝑥 2 −23𝑥+60;𝑥=3

Given a zero of the function, find the other zeroes 2. 𝑓 𝑥 = 𝑥 3 + 𝑥 2 −16𝑥−16;𝑥=4

Given a zero of the function, find the other zeroes 3. 𝑓 𝑥 = 𝑥 3 +2 𝑥 2 −20𝑥+24;𝑥=−6

Given a zero of the function, find the other zeroes 4. 𝑓 𝑥 = 2𝑥 3 +3 𝑥 2 −39𝑥−20;𝑥=4