Question

find the reminder using reminder theorem (x³+1)÷(x+1)​

Answer 1

Ans: 0

Step-by-step explanation:

The remainder theorem states that when a polynomial f(x) is divided by a linear polynomial (x−a) then the remainder of that division will be equal to p(a). If you want to evaluate the function p(x) for a given number a, you can divide the function by (x−a) and your remainder will be equal to p(a).

so let p(x)= x^3 +1

here our linear factor is

x+1

putting the value of x+1=0

then x=-1

putting the value of x in the equation p(x)

(-1)^3+1

= -1+1

=0

hence, 0 is the remainder.

Answer 2

Answer:

g ( X ) 0

= X + 1 = 0

X = -1

Now,

p ( X ) = X³ + 1

p ( -1 ) = ( -1 )³ + 1

p ( -1 ) = -1 + 1

p ( -1 ) = 0

Hence, g ( X ) is the factor of p ( X )