Hi,

f(x)=x^{4}-256

First, you need to know about this property a^{2} - b^{2}= ( a - b)( a + b) (1)

Second, you need to know about 256 that it is 4^{4}

f(x)=x^{4}-256 = x^{4}- 4^{4}= (x^{2})^{2} - (4^{2})^{2}= ( x^{2} - 4^{2} ) ( x^{2} + 4^{2}) base of above info (1)

one more time for this x^{2} - 4^{2 } you can use (1) that it means x^{2} - 4^{2}= ( x - 2 ) ( x + 2)

so f(x) = ( x^{2} - 4^{2} ) ( x^{2} + 4^{2}) = ( x - 4 ) ( x + 4) ( x^{2} + 4^{2})

f(x) = 0 it means ( x - 4 ) ( x + 4) ( x^{2} + 4^{2}) = 0 you know must be any parenthesis equals zero

x-4 = 0 ===> **x = 4** & x+4 = 0 ====> **x = -4 ** & x^{2} + 4^{2}= 0 no solution in real number but in complex number the answers will be x^{2} + 4^{2}= 0 ====> x^{2} = - 4^{2} after taking root of both sides **x = ± 4i**

**{ 4 , -4 , 4i , -4i } is set of solution**

**I hope it is useful,**

**Minoo**