Question

find the remainder when the polynomial p( x) =x ^61 + 61 is divided by x-1

Answer 1

QUESTION:

Find r (x) [Remainder] when the Polynomial $p(x) =x^{61}+ 61$  is divided by $g(x) =x-1$ -

ANSWER:

Given:

p (x) [Dividend] = $x^{61} + 61$

g (x) [Divisor] = $x -1$

To Find:

r (x) [Remainder] using the Remainder Theorem -

Remainder Theorem:-

Let p (x) be any Polynomial of Degree 1 or more & let ∝ be any Real Number. If p (x) is divided by (x - ∝), the the Remainder is p (∝)

SOLUTION:

Let g (x) = 0

g (x) = x - 1 = 0

∴ x = 1 [Zero of p (x)]

Substituting x = 1 in p (x), we get the Remainder as -

$:=>1^{61} + 61 = 1 + 61 = 62$

CONCLUSION:

r (x) = 62 is the Required Remainder of p (x)