# What are the excluded values for (12a)/(a^2-3a-10)?

Jul 31, 2017

$a = - 2 \mathmr{and} a = 5$

#### Explanation:

In the expression $\frac{12 a}{{a}^{2} - 3 a - 10}$ the denominator is a quadratic polynomial, that can be factored

${a}^{2} - 3 a - 10 = {a}^{2} + \left(2 - 5\right) a + \left(- 5\right) \left(2\right)$

$= {a}^{2} + 2 a - 5 a + \left(- 5\right) \left(2\right) = \left(a - 5\right) \left(a + 2\right)$

Then

$\frac{12 a}{{a}^{2} - 3 a - 10} = \frac{12 a}{\left(a - 5\right) \left(a + 2\right)}$

The zeroes of the polynomial in the denominator are $a = 5$ and $a = - 2$ which are the excluded values. These values are themselves excluded because you cannot divide by $0$.