Question

Xn -27 is divisible by x-3 when n is equal to

Answer 1

Hey Friend ☺

Let p ( x ) = x^n - 27

x^n - 27 is divisible by x - 3

Hence p ( 3 ) = 0

p ( 3 ) = x^n - 27

》0 = ( 3 )^n - 27

》( 3 )^n = 27

》( 3 )^n = 3^3

Therefore n = 3 .

Hope it helps you ..!!

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Answer 2

Value of n is 3.

Given:

• ${x}^{n} - 27$ is divisible by x-3.

To find:

• Find the value of n.

Solution:

Theorem to be used:

• Apply remainder theorem.
• Remainder Theorem states that p(x) is divided by (x-a) , then it's remainder is given by p(a).

Step 1:

Find the value of x from divisor.

$x - 3 = 0$

or

$\bf x = 3$

Step 2:

Put the value of x in dividend.

As remainder should be zero.

So,

${3}^{n} - 27 = 0$

or

${3}^{n} = 27$

or

${3}^{n} = {3}^{3}$

When base are same, we can equate the powers.

or

$\bf n = 3$

Thus,

Value of n is 3.

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