Polynomial Division (Long)
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Question

Divide $36x^{3}-88x^{2}+59x-19\text{ by }9x-4$.

$\begin{array}{llllllllll}& | &4x^{2}&-8x&+3&\\& | &---- &---- &---- &\\9x-4& | & 36x^{3}&-88x^{2}&+59x&-19&\\& | &\pm\,36x^{3}&\mp\,16x^{2}&\ &\\& | &---- &---- &---- &---- &\\& | &\ &-72x^{2}&+59x&-19&\\& | &\ &\mp\,72x^{2}&\pm\,32x&\\& | &---- &---- &---- &---- &\\& | &\ &\ &27x&-19&\\& | &\ &\ &\pm\,27x&\mp\,12&\\& | &---- &---- &---- &---- &\\& | &\ &\ &\ &-7&\\\end{array}$
$\;\;\;36x^{3}-88x^{2}+59x-19$
$=(9x-4)(4x^{2}-8x+3)+(-7)$
$\text{or, }\frac{36x^{3}-88x^{2}+59x-19}{9x-4}=4x^{2}-8x+3+ \frac{-7}{9x-4}$