Question

How do you factor `3x^2 - 19x +6 = 0`?

Answer 1

`0 = 3x^2-19x+6 = (3x-1)(x-6)`

Explanation:

`3x^2-19x+6=0`

Use an AC Method:

Find a pair of factors of `AC=3*6=18` with sum `B=19`

The pair `18, 1` works in that `18+1 = 19` and `18*1 = 18`.

Use this pair to split the middle term and factor by grouping:

`3x^2-19x+6 = 3x^2-18x-x+6`

`color(white)(3x^2-19x+6) = (3x^2-18x)-(x-6)`

`color(white)(3x^2-19x+6) = 3x(x-6)-1(x-6)`

`color(white)(3x^2-19x+6) = (3x-1)(x-6)`