Question

Find the remainder when x101 – 1 is divided by x -1Find the remainder when x101 – 1 is divided by x -1

Answer 1

SOLUTION

TO DETERMINE

$\sf{The \: remainder \: when \: ( {x}^{101} - 1)\: divided \: by (x - 1)}$

EVALUATION

Let

$\sf{f(x) = {x}^{101} - 1 }$

$\sf{g(x) = x - 1 }$

For Zero of the polynomial g(x) we have

$\sf{g(x) = 0 }$

$\sf{ \implies x - 1 = 0}$

$\sf{ \implies x = 1}$

Hence by the Remainder Theorem the required remainder when f(x) is divided by g(x)

$= \sf{f(1)}$

$= \sf{ {1}^{101} - 1 }$

$= \sf{1 - 1 }$

$= 0$

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Answer 2

Answer:

-100

Step-by-step explanation:

f(x) = x¹⁰¹-101

x-1=0

x=1

Remainder = p(1) , by remainder theorem

= (1)¹⁰¹-101

=1-101

=-100