# Can y= 3x^2-30x-72  be factored? If so what are the factors ?

Apr 29, 2016

Yes.
Factors are: $3 , \left(x - 12\right) , \left(x + 2\right)$

#### Explanation:

$y = 3 {x}^{2} - 30 x - 72$
By inspection, 3 is a factor $\to y = 3 \left({x}^{2} - 10 x - 24\right)$

Since the constant term is $- 24$ and the coefficient of $x$ is $- 10$, we now look for factors of $24$ which differ by $10$

These are 12 and 2.

Since the constant term is $- v e$ the constants in the factors must have different sign. Also, since the coefficient of $x$ is also $- v e$ the larger factor of $24$ must be $- v e$.

Hence the second and third factors are $\left(x - 12\right) \mathmr{and} \left(x + 2\right)$

Therefore: $y = 3 \left(x - 12\right) \left(x + 2\right)$