# Calculus/Algebra/Solutions

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