Question 114557
If one of the roots is {{{3+i}}}, then {{{3-i}}} must also be a root because complex roots come in conjugate pairs {{{a+-bi}}}.


Now that we know all three roots, namely 4, {{{3+i}}}, and {{{3-i}}}, we can create a linear binomial factor and a quadratic factor that will represent the desired degree three polynomial.


Factor 1: {{{(x-4)}}}


Factor 2: {{{(x-(3+i))(x-(3-i))}}}
{{{x^2-(3-i)x-(3+i)x+9+1}}}
{{{x^2-3x+ix-3x-ix+10}}}
{{{x^2-6x+10}}}


Complete the expression for f(x)

{{{f(x)=(x-4)(x^2-6x+10)}}}