The factors are based on the fact that "zero multiplied by anything equals zero".
When we write quadratics, cubics etc as multiplications, using the values that cause it to be zero,
the answers are embedded in the factors themselves.
x=5 can be written x-5=0...
2(x-5)=0 then x=5 since 2 is not zero....
(x-2)(x-3)=0.... x is 2 or 3 and so on.
I should have added earlier that for ax[sup:3uhuggyh]2[/sup:3uhuggyh]+bx+c, both "a" and "c" are immediately obvious,
because x(ax[sup:3uhuggyh]2[/sup:3uhuggyh]) is 3x[sup:3uhuggyh]3[/sup:3uhuggyh] and (-1)c = 1.
"b" can be discovered in 2 ways by adding together the "x" parts or the "x[sup:3uhuggyh]2[/sup:3uhuggyh]" parts,
....x(bx)-3x[sup:3uhuggyh]2[/sup:3uhuggyh]=-3x[sup:3uhuggyh]2[/sup:3uhuggyh] so b=0, or -bx-x = -x so b=0.