Ta có: \(P\left(x\right)=ax^3+bx^2+cx+d\)
*)Xét \(P\left(1\right)=a\cdot1^3+b\cdot1^2+c\cdot1+d=100\)
\(\Rightarrow a+b+c+d=100\)
*)Xét \(P\left(-1\right)=a\cdot\left(-1\right)^3+b\cdot\left(-1\right)^2+c\cdot\left(-1\right)+d=50\)
\(\Rightarrow-a+b-c+d=50\)
*)Xét \(P\left(0\right)=a\cdot0^3+b\cdot0^2+c\cdot0+d=1\)
\(\Rightarrow d=1\)
*)Xét \(P\left(2\right)=a\cdot2^3+b\cdot2^2+c\cdot2+d=120\)
\(\Rightarrow8a+4b+2c+d=120\)
Vậy ta có: \(\left\{{}\begin{matrix}a+b+c+d=100\\-a+b-c+d=50\\d=1\\8a+4b+2c+d=120\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}a=-\dfrac{227}{6}\\b=74\\c=\dfrac{377}{6}\\d=1\end{matrix}\right.\)
Vậy đa thức \(P\left(x\right)=-\dfrac{227}{6}x^3+74x^2+\dfrac{377}{6}x+1\)
\(P\left(3\right)=-\dfrac{227}{6}\cdot3^3+74\cdot3^2+\dfrac{377}{6}\cdot3+1=-166\)
