# Is it possible to factor y=x^2-12x+6 ? If so, what are the factors?

Factors of $y = {x}^{2} - 12 x + 6$ are $y = \left(x - 6 + \sqrt{30}\right) \left(x - 6 - \sqrt{30}\right)$
In $y = {x}^{2} - 12 x + 6$ discriminant is ${\left(- 12\right)}^{2} - 4 \times 1 \times 6 = 144 - 24 = 120$, which is not a perfect square of a rational number and hence we cannot factorise it easily by splitting middle term.
Hence we can use quadratic formula to first obtain zeros of function, which are $\frac{- \left(- 12\right) \pm \sqrt{120}}{2 \times 1}$ or $\frac{12 \pm 2 \sqrt{30}}{2} = 6 \pm \sqrt{30}$ and hence factors of $y = {x}^{2} - 12 x + 6$ are $y = \left(x - 6 + \sqrt{30}\right) \left(x - 6 - \sqrt{30}\right)$