Question

find the remainder when a²x² +ax + 1 is divided by ax+1
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Answer 1

a²x² +ax + 1 is divided by ax+1

remainder 1

Answer 2

ANSWER✔

$\dashrightarrow P(x)= a^2x^2+ax+1$

$\dashrightarrow g(x)= ax+1\\ \implies ax+1=0\\ \implies x= \dfrac{-1}{a}$

$\implies p\bigg( \dfrac{-1}{a} \bigg) = a^2 \bigg( \dfrac{-1}{a} \bigg)^2+ a\bigg( \dfrac{-1}{a} \bigg) +1$

$\implies p\bigg( \dfrac{-1}{a} \bigg)= a^2 \bigg( \dfrac{1}{a^2} \bigg) + \cancel{a}\:\:\bigg( \dfrac{-1}{\cancel{a}} \bigg) +1$

$\implies p\bigg( \dfrac{-1}{a} \bigg)= \cancel{a^2} \bigg( \dfrac{1}{\cancel{a^2}} \bigg) + \cancel{a}\:\:\bigg( \dfrac{-1}{\cancel{a}} \bigg)+1$

$\implies 1+(-1)+1$

$\implies 1-1+1$

$\implies 1$

$\large{\boxed{\bf{ \star\:\: remainder=1 \:\: \star}}}$

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