Question

How do you factor the expression `2x^2 - 11x + 12`?

Answer 1

`(2x - 3)(x -4)`

Explanation:

Looking at the `x^2` coefficient, `2`, we know that the coefficients of `x` in each factor can only be `1` and `2` since no other integers multiply to 2.

Therefore we can set up the factors as:
`(2x - "＿＿")*(x - "＿＿")`

We know that both of the operations in the factors must be subtraction because `12` is positive and `-11` is negative.

To find out what goes in the blanks, we need to check the factors of 12:

`1` and `12`
`2` and `6`
`3` and `4`

`1` and `12` can't work, because no matter what side each is on, `12` times anything will be greater than `11`.

`2*2 + 1*6` is `10`, and `2*6 + 1*2` is `14`, neither of which are 11.

Finally, we can try pair `3` and `4`. Feel free to try both of them yourself to see why the first must be `3` and the second must be `4`, not the other way around!