Question 118101
Remember, if a polynomial has roots of a and b, then it's factorization will be {{{(x-a)(x-b)}}}



So if a polynomial has roots of -3, 4i, and -4i (remember complex roots always come in pairs) , then it's factorization will be 


{{{(x-(-3))(x-4i)(x-(-4i))}}}



{{{(x+3)(x-4i)(x+4i)}}} Rewrite {{{x-(-3)}}} as {{{x+3}}} and {{{x-(-4i)}}} as {{{x+4i}}}



{{{(x+3)(x^2+4xi-4xi-4i^2)}}} Foil {{{(x-4i)(x+4i)}}} to get {{{x^2+4xi-4xi-4i^2}}}



{{{(x+3)(x^2-16i^2)}}} Combine like terms



{{{(x+3)(x^2-16(-1))}}} Replace {{{i^2}}} with -1



{{{(x+3)(x^2+16)}}} Multiply




{{{x^3+3x^2+16x+48}}} Now foil {{{(x+3)(x^2+16)}}} to get {{{x^3+3x^2+16x+48}}}





So the polynomial with roots of -3 and +4i is {{{x^3+3x^2+16x+48}}}