Question

13. If y^97 + 97 is divided by y + 1, the remainder is: *​

Answer 1

Given,

y+ 1 = 0

t = -1

Let f(x) = y^97 + 97

f(-1) = (-1)^97 + 97 = -1 + 97 = 96

Answer 2

The remainder is 96

Given :

$\sf \: The \: polynomial \: \: {y}^{97} + 97$

To find :

The remainder when divided by y + 1

Solution :

Step 1 of 2 :

Find zero of the polynomial y + 1

For Zero of the polynomial y + 1

We have

y + 1 = 0

⇒ y = - 1

Step 2 of 2 :

Find the remainder

$\sf \: Let\: \:f(y) = {y}^{97} + 97$

By Remainder Theorem the required Remainder when f(y) is divided by y + 1 is

= f( - 1)

$\sf = {( - 1)}^{97} + 97$

$\sf = - 1 + 97$

$\sf = 96$

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