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Polynomials — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsPolynomials2 Marks
Question
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem :
$\left(54 m^3+18 m^2-27 m+5\right) ;(m-3)$
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Answer

$p(m)=54 m^3+18 m^2-27 m+5$
Divisor $=m-3$
$\therefore$ take $m =3$
$\therefore$ By remainder theorem,
Remainder $=p(3)$
$p(m)=54 m^3+18 m^2-27 m+5$
$\therefore p(3)=54(3)^3+18(3)^2-27(3)+5$
$=54(27)+18(9)-81+5$
$=1458+162-81+5$
$\therefore \text { Remainder }=1544$

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