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Divide $a(x)$ by $b(x)$ and find the quotient $q(x)$ and remainder $r(x)$. Check your answer by showing that $q(x) b(x)+r(x)=a(x)$. (a) $a(x)=x^{4}+3 x^{3}+x+1 \quad$ and $\quad b(x)=x^{3}+2 x^{2}+2$ (b) $\quad a(x)=3 x^{4}-x^{3}+2 x^{2}+x+1 \quad$ and $\quad b(x)=3 x^{2}+2 x+1$ (c) $a(x)=x^{4}+1 \quad$ and $\quad b(x)=2 x^{2}+1$.
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