Q. 1 F5.0( 1 Vote )

Find the remainder using remainder theorem, when

8x4 + 12x3 – 2x2 – 18x + 14 is divided by x + 1

Answer :

8x4 + 12x3 – 2x2 – 18x + 14 is divided by x + 1


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) = 8x4 + 12x3 – 2x2 – 18x + 14 and we have (x + 1)


The zero of (x + 1) is – 1


Now using Remainder theorem,


p(x) = 8x4 + 12x3 – 2x2 – 18x + 14 is divided by x + 1 then, p(– 1) is the remainder


p(– 1) = 8(–1)4 + 12(–1)3 – 2(–1)2 – 18(–1) + 14


= 8 – 12 – 2 +18 + 14


= 26


Remainder = 26


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