Question

the remainder obtained when the polynomial x^64+x^27+1 is divided by x+1 is
a) 1
b)-1
c)0
d)none ​

Answer 1

Answer:

1 => ans.

Step-by-step explanation:

$x + 1 = 0 \\ x = - 1 \\ putting \: value \: of \: x \\ {( - 1)}^{64} + {( - 1)}^{27} + 1 \\ 1 - 1 + 1 \\ = 1$

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Answer 2

The remainder is 1

Given :

x⁶⁴ + x²⁷ + 1 is divided by x + 1

To find :

The remainder is

a) 1

b) - 1

c) 0

d) none

Solution :

Step 1 of 3 :

Write down the given polynomials

Here it is given that x⁶⁴ + x²⁷ + 1 is divided by x + 1

Let ,

P(x) = x⁶⁴ + x²⁷ + 1

g(x) = x + 1

Step 2 of 3 :

Find zero of g(x)

For Zero of g(x) we have

g(x) = 0

⇒ x + 1 = 0

⇒ x = - 1

Step 3 of 3 :

Find the remainder

By Remainder Theorem the required Remainder when P(x) is Q(x) is

$\sf = P( - 1)$

$\sf = {( - 1)}^{64} + {( - 1)}^{27} + 1$

$\sf = 1 - 1 + 1$

$\sf = 1$

Hence the correct option is a) 1

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