Question

please guys solve this problem and it's urgent x^6+5x^3+ 8

Answer 1

Sol:
x6 + 5x3 + 8

= (x)6+ 5x3 + 8 + x3 - x3 = x6 + 6x3 + 8 - x3       
[By adding and subtracting x3 on both sides]    
                 
= (x2)3+ (2)3+ (-x)3 - 3 × (x2) × (2) × (-x)
        
According to the identity, x3 + y3 + z3 - 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz – zx)

= (x2 + 2 - x)[(x2)2 + (2)2 + (-x)2 - (x2) × (2) - (2) × (-x) - (x2) × (-x))                                                                  

= (x2 - x + 2)(x4 + x2 + 4 - 2x2 + 2x + x3)

= (x2 - x + 2)(x4 + x3 - x2 + 2x + 4)

Thus, the facotrs of x6 + 5x3 + 8 are (x2 - x + 2)(x4 + x3 - x2 + 2x + 4).