Question

Find the remainder when x^4 -x^3 + x^2 -x +1 is divided by (x-1)​

Answer 1

Concept Used :-

Concept Used :- Remainder Theorem

• The remainder theorem in algebra states that if f(x) is a polynomial in x then the remainder on dividing f(x) by x − a is f(a).

$\large\underline{\bold{Solution :- }}$

$\rm :\longmapsto\:Let \: p(x) = {x}^{4} + {x}^{3} + {x}^{2} - x + 1$

Since,

• We have to find the remainder when p(x) is divided by x - 1

So,

By using Remainder Theorem,

• The remainder when p (x) is divided by x - 1 is given by

$\rm :\longmapsto\:remainder \: =p(1)$

$\rm :\longmapsto\:remainder \: = {1}^{4} + {1}^{3} + {1}^{2} - 1 + 1$

$\rm :\longmapsto\:remainder \: =1 + 1 + 1$

$\rm :\longmapsto\:remainder \: =3$