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

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Answer 1 · 2015-12-15T03:42:41

Yes; $x = 9 and x = - 1$ $x=9 and x=-1$

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

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

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

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

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

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

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

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

Is it possible to factor y=6x2+48x−54y=6x^2+48x-54? If so, what are the factors?