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QuestionDivide $9x^{3}-16x^{2}+11x-12\text{ by }x-1$.
Answer$\begin{array}{llllllllll}& | &9x^{2}&-7x&+4&\\& | &---- &---- &---- &\\x-1& | & 9x^{3}&-16x^{2}&+11x&-12&\\& | &\pm\,9x^{3}&\mp\,9x^{2}&\ &\\& | &---- &---- &---- &---- &\\& | &\ &-7x^{2}&+11x&-12&\\& | &\ &\mp\,7x^{2}&\pm\,7x&\\& | &---- &---- &---- &---- &\\& | &\ &\ &4x&-12&\\& | &\ &\ &\pm\,4x&\mp\,4&\\& | &---- &---- &---- &---- &\\& | &\ &\ &\ &-8&\\\end{array}$
$\;\;\;9x^{3}-16x^{2}+11x-12$
$=(x-1)(9x^{2}-7x+4)+(-8)$
$\text{or, }\frac{9x^{3}-16x^{2}+11x-12}{x-1}=9x^{2}-7x+4+ \frac{-8}{x-1}$