How to factor a fourth degree polynomial I'm working on a math problem but I am having a hard time figuring out the method used by my textbook to make this factorization:
$$x^4 + 10x^3 + 39x^2 + 70x + 50 = (x^2 + 4x + 5)(x^2 + 6x + 10)$$
I've tried to see if this equation can be factored by grouping or by long division to no avail. Any help would be greatly appreciated.

For all real $k$ we obtain:
$$x^4+10x^3+39x^2+70x+50=$$
$$=(x^2+5x+k)^2-25x^2-k^2-10kx-2kx^2+39x^2+70x+50=$$
$$=(x^2+5x+k)^2-((2k-14)x^2+(10k-70)x+k^2-50).$$
Now, we'll choose $k$ such that we'll get a difference of squares.
For which we need $$25(k-7)^2-(2k-14)(k^2-50)=0$$ or
$$(k-7)(2k^2-25k+75)=0$$ or
$$(k-7)(k-5)(2k-15)=0.$$
We see that only $k=7.5$ is valid and we obtain:
$$$x^4+10x^3+39x^2+70x+50=(x^2+5x+7.5)^2-(x^2+5x+6.25)=$$
$$=(x^2+5x+7.5)^2-(x+2.5)^2=(x^2+4x+5)(x^2+6x+10).$$
