| Factorise and divide: |
| \[55({{x}^{4}}-5{{x}^{3}}-24{{x}^{2}})\div 5x(x-8)\] |
Answer:
\[~55\left( {{x}^{4}}5{{x}^{3}}24{{x}^{2}} \right)\div 5x\text{ }\left( x8 \right)\] \[55\text{ }\left( {{x}^{4}}5{{x}^{3}}24{{x}^{2}} \right)\] \[=\text{ }55\text{ }\!\![\!\!\text{ }{{x}^{2}}({{x}^{2}}5x24)]\] \[=55[{{x}^{2}}({{x}^{2}}+3x8x24)]\] \[=\text{ }55\text{ }\!\![\!\!\text{ }{{x}^{2}}(x+3)(x8)]\] \[=5\times 11{{x}^{2}}\left( x+3 \right)\left( x8 \right)\] Now, Dividing by \[5x\left( x8 \right)\] \[\frac{5\times 11{{x}^{2}}(x+3)(x-8)}{5x(x-8)}=11x(x+3)\]
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