Q. 35.0( 3 Votes )

Check whether x +

Answer :

Let p(x) = x3 + 3x2 + 3x + 1


If after dividing x3 + 3x2 + 3x + 1 by x + 1 the remainder is 0 then x + 1 is a factor of x3 + 3x2 + 3x + 1


Now we will find remainder using remainder theorem which states that


If a polynomial p(x) is divided by a polynomial x – a then the remainder is p(a)


x + 1 can be written as x – (-1)


compare x – (-1) with x – a we get a = -1


p(a) = p(-1)


Substitute -1 in x3 + 3x2 + 3x + 1


p(-1) = (-1)3 + 3(-1)2 + 3(-1) + 1


p(-1) = -1 + 3 – 3 + 1


p(-1) = 0


As the remainder is 0 hence x + 1 is a factor of x3 + 3x2 + 3x + 1


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