1.2 – Factoring Polynomial Using the Remainder Theorem · 2019-11-05 · The Remainder Theorem:...
Transcript of 1.2 – Factoring Polynomial Using the Remainder Theorem · 2019-11-05 · The Remainder Theorem:...
PreCalculus 12
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1.2–FactoringPolynomialUsingtheRemainderTheorem
WhatistheremainderwhenP(x)=x3+5x–10isdividedbyx–2?
LongDivision: SyntheticDivision:
or,substitutex=2intothepolynomialP(x):
Why?Rememberthemultiplicationstatement:
The Remainder Theorem:
When Polynomial P(x) is divided by divisor (x – a), the remainder will be __________.
PreCalculus 12
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Example:
a) UsetheremaindertheoremtodeterminetheremainderwhenP(x)=x3–10x+6isdividedbyx+4.
b) Verifyyouranswerwithsyntheticdivision.
OnyourOwn:Findtheremainderof(x16–9x6+x2+9)÷(x+1)
Example:Findtheremainderof(4x2–3x+6)÷(2x-1)
PreCalculus 12
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Sinceweknowthatdividingapolynomial!(#)by # − & willresultinaremainderof!(&)wecanusethisknowledgetosolveforunknownswithinthepolynomial!(#):
Example:FindkifP(x)=x3+2x2–8x+kdividedby(x-3)givesaremainderof17.
Wecanalsousethisinformationtocheckifaspecificbinomialisa______________________oftheoriginalpolynomial!(#).
Ø Ifitisafactorthentheremainderwillbe_________________
Example:Whichofthefollowingbinomialsarefactorsofthepolynomial! # = #) + 2#, − 13# + 10?
a) # − 1b) # − 2c) # + 3
Assignment:P.21#1-4,6(i-iv),7,8