Ta có: P(x)=ax3+bx2+cx+d
*)Xét P(1)=a⋅13+b⋅12+c⋅1+d=100
⇒a+b+c+d=100
*)Xét P(−1)=a⋅(−1)3+b⋅(−1)2+c⋅(−1)+d=50
⇒−a+b−c+d=50
*)Xét P(0)=a⋅03+b⋅02+c⋅0+d=1
⇒d=1
*)Xét P(2)=a⋅23+b⋅22+c⋅2+d=120
⇒8a+4b+2c+d=120
Vậy ta có: \(\left\{{}\begin{matrix}\text{a+b+c+d=100}\\\text{−a+b−c+d=50}\\\text{d=1}\\\text{8a+4b+2c+d=120 }\end{matrix}\right.\)⇒\(\left\{{}\begin{matrix}a=\dfrac{-227}{6}\\b=74\\c=\dfrac{377}{6}\\d=1\end{matrix}\right.\)
Vậy đa thức P(x)=\(\dfrac{-227}{6}x^3+74x^2+\dfrac{377}{6}x+1\)
P(3)=\(\dfrac{-227}{6}.3^3+74.3^2+\dfrac{377}{6}.3+1=-166\)
CHÚC BN HỌC TỐT ^-^