Q. 1 G4.0( 3 Votes )

Find the remainder using remainder theorem, when

x3 – ax2 – 5x + 2a is divided by x – a

Answer :

x3 – ax2 – 5x + 2a is divided by x – a


Remainder theorem states that if p(x) is any polynomial and a is any real number and If p(x) is divided by the linear polynomial (x – a) , then the remainder is p(a).


Let p(x) = x3 – ax2 – 5x + 2a and we have (x – a)


The zero of (x – a) is a


Now using Remainder theorem,


p(x) = x3 – ax2 – 5x + 2a is divided by x – a then, p(a) is the remainder


p(a) = (a)3 – a(a)2 – 5(a) + 2a


= a3 – a3 – 5a+ 2a


= – 3a


Remainder = –3a


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