Question 133001
A quadratic equation {{{ax^2+bx+c=0}}} has {{{p}}} as a root if and only if {{{x-p}}} is a factor of the polynomial {{{ax^2+bx+c}}}.  Since the Fundamental Theorem of Algebra tells us that a 2nd degree equation must have 2 roots, the root 8 must have a multiplicity of 2, in other words there are two roots and they are both 8.  Therefore, the factors of the polynomial must be {{{(x-8)(x-8)}}}.


Apply FOIL:
{{{x^2-16x+64}}}


And set the polynomial equal to zero:
{{{x^2-16x+64=0}}}