Question 1198420
 Find a polynomial of 

degree {{{3 }}}
zeros of :
{{{x[1]=-3}}}
{{{x[2]=-1}}}
​ {{{x[3]=4}}}

 for which {{{f(-2)=-30}}}


{{{f(x)=a(x-x[1])(x-x[2])(x-x[3])}}}

{{{f(x)=a(x-(-3))(x-(-1))(x-4)}}}

{{{f(x)=a(x+3)(x+1)(x-4)}}}

{{{f(x)=a(x^3 - 13x - 12)}}}........if {{{f(-2)=-30}}},  we have


{{{-30=a((-2)^3 - 13(-2)  - 12)}}}

{{{-30=a(6)}}}

{{{a=-30/6}}}

{{{a=-5}}}


and your polynomial is


{{{f(x)=-5(x^3 - 13x - 12)}}}

{{{f(x)=-5x^3 + 65x + 60}}}