Calculus/Algebra/Solutions

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1. Factor x-1 out of 6x^3-4x^2+3x-5.
\begin{array}{rl}&~~\,6x^2+2x+5\\
x-1\!\!\!\!&\big)\!\!\!\begin{array}{lll}
\hline
\,6x^3-4x^2+3x-5
\end{array}\\
&\!\!\!\!-\underline{(6x^3-6x^2)~~~}\\
&\!\!\!\!~~~~~~~~~~~~2x^2+3x-5~~~\\
&\!\!\!\!~~~~~~~~-\underline{(2x^2-2x)~~~}\\
&\!\!\!\!~~~~~~~~~~~~~~~~~~~~~5x-5~~~\\
&\!\!\!\!~~~~~~~~~~~~~~~~-\underline{(5x-5)~~~}\\
&\!\!\!\!~~~~~~~~~~~~~~~~~~~~~~~~~~~~0~~~\\
\end{array}

\mathbf{6x^3-4x^2+3x-5=(x-1)(6x^2+2x+5)}