Question

find the remainder when x^4+1 is divided by x-1 using remainder theorem​

Answer 1

GIVEN :-

• p(x) = x⁴ + 1.

TO FIND :-

• The Remainder by Remainder theorem.

SOLUTION :-

◉ Let x - 1 = 0.

◉ x = 1.

☯ BY REMAINDER THEOREM,

➠ Remainder theorem :- If p(x) is is any polynomial of degree greater than or equal to 1 and p(x) is divided by the linear polynomial x - a , Then the reminder is p(a).

➬ p(x) = x⁴ + 1.

➬ p(1) = (1)⁴ + 1

➬ 1 + 1

➬ 2.

Hence the Remainder is 2.

ADDITIONAL INFORMATION :-

➠ Factor theorem :- x - a is a factor of the polynomial p(x) , If p(a) = 0. Also, If x - a is a Factor of p(x) , Then p(a) = 0.

➠Every linear polynomial in one variable has a unique zero, a non - zero constant polynomial has no zero, and every real number is a zero of the zero polynomial.

Answer 2

Answer:

remainder = 2

Step-by-step explanation:

Remainder theorem

d(x) = g(x)*q(x)+r(x)

x⁴+1= (x-1)(x³+x²+x+1)+ r(x)

x⁴+1 = (x⁴+x³+x²+x-x³-x²-x-1)+ r(x)

x⁴+1 = (x⁴-1) +r(x)

x⁴+1-x⁴+1 = r(x)

r(x) = 2

Hope it helped you......