Polynomial Division (Long)

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Divide $9x^{3}+28x^{2}-4\text{ by }x+3$.

**Answer**

$\begin{array}{llllllllll}& | &9x^{2}&+x&-3&\\& | &---- &---- &---- &\\x+3& | & 9x^{3}&+28x^{2}&\ &-4&\\& | &\pm\,9x^{3}&\pm\,27x^{2}&\ &\\& | &---- &---- &---- &---- &\\& | &\ &x^{2}&\ &-4&\\& | &\ &\pm\,x^{2}&\pm\,3x&\\& | &---- &---- &---- &---- &\\& | &\ &\ &-3x&-4&\\& | &\ &\ &\mp\,3x&\mp\,9&\\& | &---- &---- &---- &---- &\\& | &\ &\ &\ &5&\\\end{array}$

$\;\;\;9x^{3}+28x^{2}-4$

$=(x+3)(9x^{2}+x-3)+(5)$

$\text{or, }\frac{9x^{3}+28x^{2}-4}{x+3}=9x^{2}+x-3+ \frac{5}{x+3}$