question_answer

      Divide 63 \[\left( {{p}^{4}}+5{{p}^{3}}-24{{p}^{2}} \right)\text{ }by\text{ }9p\left( p+8 \right)\]

Answer:

We have, \[63({{p}^{4}}+5{{p}^{3}}-24{{p}^{2}})\div 9p(p+8)\]

\[=\frac{63({{p}^{4}}+5{{p}^{3}}-24{{p}^{2}})}{9p(P+8)}\]

\[=\frac{63{{p}^{2}}({{p}^{2}}+5p-24)}{9p(p+8)}\]

\[=\frac{63{{p}^{2}}}{9p}\left[ \frac{({{p}^{2}}+5p-24)}{(p+8)} \right]\]

\[=7p\left[ \frac{{{p}^{2}}+8p-3p-24}{p+8} \right]\]

\[=7p\left[ \frac{p(p+8)-3(p+8)}{(p+8)} \right]\]

\[=7p\left[ \frac{(p+8)(p-3)}{(p+8)} \right]\]

\[=7p(p-3)\].