Factoring Problem

[JJimenez]

Question asks to factor completely:
(x²-2)^5/2+2x(x²-2)^3/2+x²(x²-2)^1/2

So far I have:
2(x²-2)(x²-2)^1/2+2x(x²-2)(x²-2)^1/2+x²(x²-2)^1/2
[(2x-2)(2x+2)+(2x)(x²-4)+x²](x²-2)^1/2
[(2x-2)(2x+2)+(2x)(x+2)(x-2)+x²](x²-2)^1/2

This is where I'm stuck at. Any help would be greatly appreciated .

 

[Deleted member 4993]

Question asks to factor completely:
(x²-2)^5/2+2x(x²-2)^3/2+x²(x²-2)^1/2

So far I have:
2(x²-2)(x²-2)^1/2+2x(x²-2)(x²-2)^1/2+x²(x²-2)^1/2
[(2x-2)(2x+2)+(2x)(x²-4)+x²](x²-2)^1/2
[(2x-2)(2x+2)+(2x)(x+2)(x-2)+x²](x²-2)^1/2

This is where I'm stuck at. Any help would be greatly appreciated .

(x²-2)^5/2+2x(x²-2)^3/2+x²(x²-2)^1/2

= [(x²-2)²+2x(x²-2) + x²](x²-2)^1/2


= [(x⁴-4x² +4)+ (2x³-4x) + x²](x²-2)^1/2

= [x⁴- 3x² + 2x³-4x + 4] (x²-2)^1/2

By observation, you can find that x-1 is a factor of the polynomial.

Then continue.....