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This is basically a quadratic equation, so here we will us middle term splitting method, which is shown below

That is: - x^2 + 6x + 8x + 48

Therefore x(x+6) + 8(x+6) = 0

So (x+8) (x+6) = 0

From above equation we have seen that x = -8 and x = -6 is the required solution of the given equation.

There is basically no common factor in above equation for all four terms. But it is quite clear that there is some common factor between first and second term and also between third and fourth term. So we will take common accordingly

Therefore x^3 + 11 x^2 + 11 x + 121

= x^2 (x+ 11) + 11 (x+11)

Now we can see that (x+11) can be taken out

So x^3 + 25x^2 + 25x + 625= (x+11) (x^2 +11)