Basic functions: Rational functions
Polynomial division with remainder
Consider \[\begin{aligned}p(x)&=-4\,x^4+4\,x^3-8\,x^2+4\,x-2\\[0.25cm] d(x)&=2\,x^2+1\end{aligned}\] Divide \(p(x)\) by \(d(x)\) with remainder, that is, determine the quotient \(q(x)\) and the remainder \(r(x)\) such that \(p(x)=q(x)\cdot d(x)+r(x)\).
| quotient \(q(x)={}\) |
| remainder \(r(x)={}\) |
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