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