Divide   \( 5x^2-9x+3 \quad by \quad (x+1)\)

	\(5x\)	\(-14\)
\(x\)	\(5x^2\)	\(-14x\)
\(1\)	\(5x\)	\(-14\)

\begin{align} Quotient & = 5x-14 \\ Remainder & = 17 \\ \\ So \quad 5x^2 -9x+3 & = (5x-14)(x+1) +17 \end{align}

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Divide   \( 4x^3+10x^2-3x -6 \quad by \quad (x-2)\)

	\(4x^2\)	\(18x\)	\(33\)
\(x\)	\(4x^3\)	\(18x^2\)	\(33x\)
\(-2\)	\(-8x^2\)	\(-36x\)	\(-66\)

\begin{align} Quotient & = 4x^2+18x+33 \\ Remainder & = 60 \\ \\ So \quad 4x^3 +10x^2 -3x-6 & = (4x^2+18x+33)(x-2) +60 \end{align}

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Divide   \( 6x^4+3x^3-4x^2+x +5 \quad by \quad (x^2-2x+1)\)

	\(6x^2\)	\(15x\)	\(20\)
\(x^2\)	\(6x^4\)	\(15x^3\)	\(20x^2\)
\(-2x\)	\(-12x^3\)	\(-30x^2\)	\(-40x\)
\(1\)	\(6x^2\)	\(15x\)	\(20\)

\begin{align} Quotient & = 6x^2+15x+20 \\ Remainder & = 26x-15 \\ \\ 6x^4+3x^3 -4x^2+x+5 & = (6x^2+15x+20)(x^2-2x+1) + 26x-15 \end{align}