\(a,\Leftrightarrow x^3+3x^2+5x+a=\left(x+3\right).a\left(x\right)\)
Thay \(x=-3\Leftrightarrow-27+27-15+a=0\Leftrightarrow a=15\)
\(b,\Leftrightarrow-3x^3+5x^2-9x+a=\left(-3x+5\right).b\left(x\right)\)
Thay \(x=\dfrac{5}{3}\Leftrightarrow-\dfrac{125}{9}+\dfrac{125}{9}-15+a=0\Leftrightarrow a=15\)
\(c,\Leftrightarrow x^4+3x^3-x^2+ax+b=\left(x^2+2x-3\right).c\left(x\right)=\left(x+3\right)\left(x-1\right).c\left(x\right)\)
Thay \(x=-3\Leftrightarrow81-81-9-3a+b=0\Leftrightarrow3a-b=-9\left(1\right)\)
Thay \(x=1\Leftrightarrow1+3-1+a+b=0\Leftrightarrow a+b=-3\left(2\right)\)
\(\left(1\right)\left(2\right)\Leftrightarrow\left\{{}\begin{matrix}a=-3\\b=0\end{matrix}\right.\\ d,\Leftrightarrow x^3+3x^2-2x+a=\left(x+2\right).d\left(x\right)+5\)
Thay \(x=-2\Leftrightarrow-8+12+4+a=5\Leftrightarrow a=-3\)
