Question

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

Answer 1

Factors of `y=x^2-12x+6` are `y=(x-6+sqrt30)(x-6-sqrt30)`

Explanation:

In `y=x^2-12x+6` discriminant is `(-12)^2-4xx1xx6=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 `(-(-12)+-sqrt120)/(2xx1)` or `(12+-2sqrt30)/2=6+-sqrt30` and hence factors of `y=x^2-12x+6` are `y=(x-6+sqrt30)(x-6-sqrt30)`