Question

X^36+36 is divided by (X+1),find the remainder

Answer 1

Given that (x + 1) is the factor of given equation,


So, by Remainder theorem

x = - 1




x^(36) + 36 = remainder

=>1^(36) + 36 = remainder

=> 1 + 36= Remainder

=> 37 = Remainder

Answer 2

The required Remainder = 37

Given :

$\sf The \: polynomial \: \: {x}^{36} + 36$

To find :

The remainder when divided by x + 1

Solution :

Step 1 of 2 :

Find zero of the polynomial x + 1

For Zero of the polynomial

x + 1 = 0

⇒ x = - 1

Zero of the polynomial x + 1 is - 1

Step 2 of 2 :

Find the required Remainder

$\sf Let \: \: p(x) = {x}^{36} + 36$

By Remainder Theorem the required Remainder when p(x) is divided by x + 1

$\sf= p( - 1)$

$\sf = {( - 1)}^{36} + 36$

$\sf = 1+ 36$

$\sf = 37$

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