Question
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem :
$\left(2 x^3-2 x^2+a x-a\right) ;(x-a)$
$\left(2 x^3-2 x^2+a x-a\right) ;(x-a)$
✓
Answer
$p(x)=2 x^3-2 x^2+a x-a$
Divisor $=x-a$
$\therefore$ take $x = a$
By remainder theorem,
Remainder $=p(a)$
$p(x)=2 x^3-2 x^2+a x-a$
$\therefore p ( a )=2 a ^3-2 a ^2+ a ( a )- a$
$=2 a^3-2 a^2+a^2-a$
$\therefore$ Remainder $=2 a^3-a^2-a$
Divisor $=x-a$
$\therefore$ take $x = a$
By remainder theorem,
Remainder $=p(a)$
$p(x)=2 x^3-2 x^2+a x-a$
$\therefore p ( a )=2 a ^3-2 a ^2+ a ( a )- a$
$=2 a^3-2 a^2+a^2-a$
$\therefore$ Remainder $=2 a^3-a^2-a$
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