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) $Q(x)=2 x^{2}-2 x ; \quad R(x)=-6 x$

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Answer

$Q(x)=2 x^{2}-2 x+1 ; \quad R(x)=-6 x+2$

Steps

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 ：$Q(x)=2 x^{2}-2 x+1 ; \quad R(x)=-6 x+2$