Question

If x51 +51 is divided by x+1 then remainder is ​

Answer 1

Answer:

$f(x) ={x}^{51} + 51\\g(x) = x + 1 \\ x + 1 = 0 \\ x = 0 - 1 \\ x = - 1 \\ f( - 1) = { - 1}^{51} + 51 \\ = - 1 + 51 \\ = 50 \\ \\ therefore \: the \: remainder \: is \: 50.$

Answer 2

Step-by-step explanation:

Given polynomial p(x)= x⁵¹+51

Given divisor =x+1

we know that by Remainder theorem,

Let p(x) be a polynomial of degree greater than or equal to 1 and x-a is another linear polynomial then if p(x) is divided by x-a then the remainder is p(a).

Given p(x) is divided by x+1 then remainder is p(-1).

now,

p(-1)=(-1)⁵¹+51

=>p(-1)=-1+51

=>p(-1)=50

The remainder is 50