Question 1154246
Too many for just one single posting.
Maybe say exactly what you have trouble to understand.


Picking just {{{-x^3+22x^2-121x=0}}}

{{{-x(x^2-22x+121)=0}}}, and recognize how the 22 and the 121 are related;
{{{-x(x-11)(x-11)=0}}}


Very obviously, either x=0  or x=11.




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Look very carefully:
{{{x^2-22x+121}}}
{{{x^2-22x+11*11}}}
{{{x^2-11x-11x+(-11)(-11)}}}
{{{(x-11)(x-11)}}}
{{{(x-11)^2}}}
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or if starting from the binomial to be multiplied,
{{{(x-11)x-(x-11)11}}}
{{{x^2-11x-11x-(-121)}}}
{{{x^2-22x+121}}}, the quadratic started from.