Question 211171
You're off to a great start. I'll start where you left off.



{{{(x^2-9x+20)(x-6)=0}}} Start with the given equation.



{{{(x-6)(x^2-9x+20)=0}}} Rearrange the terms.



{{{x(x^2-9x+20)-6(x^2-9x+20)=0}}} Expand. Note: {{{(A+B)(C+D+E)=A(C+D+E)+B(C+D+E)}}}



{{{x(x^2)-x(9x)+x(20)-6(x^2)-6(-9x)-6(20)=0}}} Distribute



{{{x^3-9x^2+20x-6x^2+54x-120=0}}} Multiply



{{{x^3-15x^2+74x-120=0}}} Combine like terms.



So {{{(x^2-9x+20)(x-6)=x^3-15x^2+74x-120}}}



This means that the polynomial with the roots {{{r[1]=4}}}, {{{r[2]=5}}}, and {{{r[3]=6}}} is {{{y=x^3-15x^2+74x-120}}}