2.3 Long and Synthetic Division of polynomials

Vocab: long division, synthetic division, remainder theorem, factor theorem, divisor, quotient, dividend, remainder

Objectives: to be able to use long division to divide polynomials by other polynomials; use synthetic division to divide polynomials by binomials of the form (x-k), and use the remainder and factor theorems.

2.3

How do I use Long division To find the quotient of two numbers?

Ex. 1 186 ÷ 7

186 7

divisor

dividend

quotient

2.3

How do I use Long division To find the quotient of two Polynomials?

Ex. 2 2𝑥3 − 8𝑥2 + 13𝑥 − 10 ÷ (𝑥 − 2)

divisor

dividend

quotient

2𝑥3 − 8𝑥2 + 13𝑥 − 10 𝑥 − 2

2.3

How do I use Long division To find the quotient of two Polynomials?

Ex. 3 −5𝑥2 −2 + 3𝑥 + 2𝑥4 + 4𝑥3 ÷ (2𝑥 − 3 + 𝑥2)

2.3 Synthetic Division

How do I use synthetic division to find the quotient of Polynomials?

2𝑥3 − 8𝑥2 + 13𝑥 − 10 ÷ (𝑥 − 2) Ex. 4

2.3 Remainder Theorem

How do I use The remainder Theorem to evaluate a polynomial function.

Ex. 5 𝐸𝑣𝑎𝑙𝑢𝑎𝑡𝑒 𝑓 𝑥 = 4𝑥3 + 10𝑥2 − 3𝑥 − 8 @ 𝑓(4)

2.3 Remainder Theorem

How do I use the factor theorem to show that a a binomial is a factor of a polynomial and to find the remaining factors?

Ex. 6 𝑆ℎ𝑜𝑤 𝑡ℎ𝑎𝑡 𝑥 + 3 𝑖𝑠 𝑎 𝑓𝑎𝑐𝑡𝑜𝑟 𝑜𝑓 𝑓 𝑥 = 𝑥3 − 19𝑥 − 30 , Then find the remaining factors.

Extra example of long division

Extra example of synthetic division

HW problems

• Pages 14413,15,23,24,27,35,45,47, 55a, 55c,59, 61,69