Question

How do you factor `2n^2 - 7n + 3`?

Answer 1

`(2x-1)(x-3)`

Explanation:

The general equation that factors as `(ax+b)(cx+d)` multiplies out to be `acx^2+(ad+bc)x+bd`. This shows that the coefficient of the middle term is made up from factors of the coefficients of the outer terms.

Thus is this case we need factors of `2` and `(-3)` that will add (or subtract) to give `-7`.

The only possible factors are `2` and `1`, and `3` and `1`.

The result is therefore `(2x-1)(x-3)`