$a)$

$\{\begin{array}{l}w\left(0\right)=5\\ w\left(1\right)=-3\end{array}$

$\{\begin{array}{l}-2\cdot 0^3+3\cdot 0^2+a\cdot 0+b=5\\ -2\cdot 1^3+3\cdot 1^2+a\cdot 1+b=-3\end{array}$

$\{\begin{array}{l}b=5\\ -2+3+a+b=-3\end{array}$

$\{\begin{array}{l}b=5\\ a=-3-1-b=-4-5=-9\end{array}$

 

 

 

 

$b)$

$\{\begin{array}{l}w\left(-3\right)=11\\ w\left(2\right)=\frac{8}{3}\end{array}$

$\{\begin{array}{l}a\cdot {\left(-3\right)}^3+{\left(-3\right)}^2+b\cdot \left(-3\right)+2=11\\ a\cdot 2^3+2^2+b\cdot 2+2=\frac{8}{3}\end{array}$

$\{\begin{array}{l}-27a+9-3b+2=11\mid -11\\ 8a+4+2b+2=\frac{8}{3}\mid \cdot 3\end{array}$

$\{\begin{array}{l}-27a-3b=0\mid +3b\\ 24a+6b+18=8\mid -18\end{array}$

$\{\begin{array}{l}3b=-27a\mid :3\\ 24a+6b=-10\end{array}$

$\{\begin{array}{l}b=-9a\\ 24a+6\cdot \left(-9a\right)=-10\end{array}$

$\{\begin{array}{l}b=-9a\\ -30a=-10\mid :\left(-30\right)\end{array}$

$\{\begin{array}{l}b=-9a\\ a=\frac{1}{3}\end{array}$

$\{\begin{array}{l}b=-9\cdot \frac{1}{3}=-3\\ a=\frac{1}{3}\end{array}$

 

 

 

 

$c)$

$\{\begin{array}{l}w\left(2\right)=-w\left(1\right)\\ w\left(-2\right)=16\end{array}$

$\{\begin{array}{l}{2}^4+a\cdot 2^3+b\cdot 2^2-10=-\left(1^4+a\cdot 1^3+b\cdot 1^2-10\right)\\ {\left(-2\right)}^4+a\cdot {\left(-2\right)}^3+b\cdot {\left(-2\right)}^2-10=16\end{array}$

$\{\begin{array}{l}16+8a+4b-10=-\left(1+a+b-10\right)\\ 16-8a+4b-10=16\mid -6\end{array}$

$\{\begin{array}{l}6+8a+4b=9-a-b\mid -6+a+b\\ -8a+4b=10\mid +8a\end{array}$

$\{\begin{array}{l}9a+5b=3\\ 4b=10+8a\mid :4\end{array}$

$\{\begin{array}{l}9a+5b=3\\ b=2\frac{1}{2}+2a\end{array}$

$\{\begin{array}{l}9a+5\left(2\frac{1}{2}+2a\right)=3\\ b=2\frac{1}{2}+2a\end{array}$

$\{\begin{array}{l}9a+12\frac{1}{2}+10a=3\mid -12\frac{1}{2}\\ b=2\frac{1}{2}+2a\end{array}$

$\{\begin{array}{l}19a=-9\frac{1}{2}\\ b=2\frac{1}{2}+2a\end{array}$

$\{\begin{array}{l}a=-9\frac{1}{2}:19=-\frac{19}{2}:19=-\frac{1}{2}\\ b=2\frac{1}{2}+2\cdot \left(-\frac{1}{2}\right)=2\frac{1}{2}-1=1\frac{1}{2}\end{array}$