<s>[INST] I need to define the cubic equation $f(x)= ax^3 + bx^2 + cx + d$ It is given that if cubic function $f(x)$ is divided by $(x^2+4)$ and $(x+3)$, the remainders will be $7x-20$ and $-2$ respectively. Also it is said show that $f(x)$ is $x^3 + 6x^2 + 11x +4$. I tried but can i find the $a,b,c$, and $d$ without knowing them in from the start?
 [/INST] $f(x) = (x^2 + 4)(ax +b) +7x - 20$
$f(-3)=-2 = 13(-3a+b)-41 $
therefore $b= 3a+3$ 
so, $f(x)= (x^2+4)(ax +3a+3)+ 7x-20 $  (non-zero $a$) 
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