Polynomial Division (Long)

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Divide $63x^{3}+33x^{2}-34x-3\text{ by }7x-1$.

**Answer**

$\begin{array}{llllllllll}& | &9x^{2}&+6x&-4&\\& | &---- &---- &---- &\\7x-1& | & 63x^{3}&+33x^{2}&-34x&-3&\\& | &\pm\,63x^{3}&\mp\,9x^{2}&\ &\\& | &---- &---- &---- &---- &\\& | &\ &42x^{2}&-34x&-3&\\& | &\ &\pm\,42x^{2}&\mp\,6x&\\& | &---- &---- &---- &---- &\\& | &\ &\ &-28x&-3&\\& | &\ &\ &\mp\,28x&\pm\,4&\\& | &---- &---- &---- &---- &\\& | &\ &\ &\ &-7&\\\end{array}$

$\;\;\;63x^{3}+33x^{2}-34x-3$

$=(7x-1)(9x^{2}+6x-4)+(-7)$

$\text{or, }\frac{63x^{3}+33x^{2}-34x-3}{7x-1}=9x^{2}+6x-4+ \frac{-7}{7x-1}$