Question

What is the remainder when (x^4+36) is divided by (x^2-8)

Answer 1

100..........................

Answer 2

Answer:

The remainder is 100.

Step-by-step explanation:

The divisor is $x^2-8$.

Dividend is $x^4+36$.

We have to find the remainder of

$\frac{x^4+36}{x^2-8}$

It can be written as

$\frac{x^4+36}{x^2-8}=\frac{x^4-64+64+36}{x^2-8}$

$\frac{x^4+36}{x^2-8}=\frac{(x^4-64)+100}{x^2-8}$

$\frac{x^4+36}{x^2-8}=\frac{(x^4-64)}{x^2-8}+\frac{100}{x^2-8}$

$\frac{x^4+36}{x^2-8}=\frac{(x^2-8)(x^2+8)}{x^2-8}+\frac{100}{x^2-8}$       $[\because a^2-b^2=(a-b)(a+b)]$

$\frac{x^4+36}{x^2-8}=x^2+8+\frac{100}{x^2-8}$

Therefore the remainder is 100.