2a^3+a^2−17a−190 divide by (a-3)/2
You asked:
Evaluate the expression: \(2 \cdot {a}^{3} + {a}^{2} - 17 a - \frac{190}{\frac{a - 3}{2}}\)
MathBot Answer:
Evaluated
\(\displaystyle 2 \cdot {a}^{3} + {a}^{2} - 17 a - \frac{190}{\frac{a - 3}{2}} = 2 a^{3} + a^{2} - 17 a - \frac{190}{\frac{a}{2} - \frac{3}{2}} \)
Expanded
\[2 \cdot {a}^{3} + {a}^{2} - 17 a - \frac{190}{\frac{a - 3}{2}} = 2 a^{3} + a^{2} - 17 a - \frac{190}{\frac{a}{2} - \frac{3}{2}}\]
Factored
\[2 \cdot {a}^{3} + {a}^{2} - 17 a - \frac{190}{\frac{a - 3}{2}} = \frac{\left(a - 5\right) \left(2 a^{3} + 5 a^{2} + 5 a + 76\right)}{a - 3}\]