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Question Number 61261 by Jmasanja last updated on 31/May/19

for polynomial p(x),the value of   p(3) is −2.which of the following   must be true about p(x)?  (a)x−5 is the factor of p(x)  (b)x−2is the factor of p(x)  (c)x+2 is the factor of p(x)  (d)the reminder when  p(x) is divide  d by x−3 is −2

$${for}\:{polynomial}\:{p}\left({x}\right),{the}\:{value}\:{of}\: \\ $$$${p}\left(\mathrm{3}\right)\:{is}\:−\mathrm{2}.{which}\:{of}\:{the}\:{following}\: \\ $$$${must}\:{be}\:{true}\:{about}\:{p}\left({x}\right)? \\ $$$$\left({a}\right){x}−\mathrm{5}\:{is}\:{the}\:{factor}\:{of}\:{p}\left({x}\right) \\ $$$$\left({b}\right){x}−\mathrm{2}{is}\:{the}\:{factor}\:{of}\:{p}\left({x}\right) \\ $$$$\left({c}\right){x}+\mathrm{2}\:{is}\:{the}\:{factor}\:{of}\:{p}\left({x}\right) \\ $$$$\left({d}\right){the}\:{reminder}\:{when}\:\:{p}\left({x}\right)\:{is}\:{divide} \\ $$$${d}\:{by}\:{x}−\mathrm{3}\:{is}\:−\mathrm{2} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Answered by tanmay last updated on 31/May/19

p(x)=(x−3)q(x)+R(x)  p(3)=(3−3)q(3)+R(3)  p(3)=R(3)=−2   [remainder=−2]

$${p}\left({x}\right)=\left({x}−\mathrm{3}\right){q}\left({x}\right)+{R}\left({x}\right) \\ $$$${p}\left(\mathrm{3}\right)=\left(\mathrm{3}−\mathrm{3}\right){q}\left(\mathrm{3}\right)+{R}\left(\mathrm{3}\right) \\ $$$${p}\left(\mathrm{3}\right)={R}\left(\mathrm{3}\right)=−\mathrm{2}\:\:\:\left[{remainder}=−\mathrm{2}\right] \\ $$

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