# Is it possible to factor y=6x^2+48x-54? If so, what are the factors?

Dec 15, 2015

Yes; $x = 9 \mathmr{and} x = - 1$

#### Explanation:

Factoring $A {x}^{2} + B x + C$
Find factors of $A C$ that add up to $B$

Original equation:
$y = 6 {x}^{2} + 48 x - 54$

Simplify by factoring out $6$:
y=6(x^2+8-9)

Multiply $A$ by $C$:
1•(-9)#
$- 9$
x
Find factors of $- 9$
$1 , - 9$
$9 , - 1$
$3 , - 3$

Determine which of the factors add up to $B .$ Here, $B = 8$.

The two factors that add up to $8$ are $9 , - 1$.

Now, you can plug the factors back into the equation.
$y = 6 \left(x + 9\right) \left(x - 1\right)$

Or you can set the factors equal to zero and solve for $x$
You should end up with $x = 1$ and $x = - 9$.