Problem
Performing the division $\frac{2 x^{4}-3 x^{2}-3 x+1}{x^{2}+x-1}$, the quotient $Q(x)$ and remainder $R(x)$ are: A) $Q(x)=2 x^{2}-2 x+1 ; \quad R(x)=-6 x+2$ B) $Q(x)=2 x^{2}+2 x+1 ; \quad R(x)=6 x+2$ C) $Q(x)=2 x^{2}+2 x-1 ; \quad R(x)=6 x-2$ D) $Q(x)=2 x^{2}-2 x-1 ; \quad R(x)=-6 x-2$ E) $Q(x)=2 x^{2}-2 x ; \quad R(x)=-6 x$
Solution
Step 1 ：Performing the division \(\frac{2 x^{4}-3 x^{2}-3 x+1}{x^{2}+x-1}\), the quotient \(Q(x)\) and remainder \(R(x)\) are:
Step 2 ：\(Q(x)=2 x^{2}-2 x+1 ; \quad R(x)=-6 x+2\)
