2.3 Long and Synthetic Division of polynomials · Vocab: long division, synthetic division,...
Transcript of 2.3 Long and Synthetic Division of polynomials · Vocab: long division, synthetic division,...
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