Question

How do you factor completely `x^2+2x+3x+6`?

Answer 1

Factor by grouping to find:

`x^2+2x+3x+6=(x+3)(x+2)`

Explanation:

Factor by grouping as follows:

`x^2+2x+3x+6`

`=(x^2+2x)+(3x+6)`

`=x(x+2)+3(x+2)`

`=(x+3)(x+2)`

With this question, the hard/fun part has already been done for you, viz splitting the `x` term into `2x+3x`. Normally you would be given something like `x^2+5x+6` and have to find the split yourself.

If you did have to find the split yourself, you would look for two numbers which add up to `5` and multiply together to give `6`.

Notice that in general, `(x+a)(x+b) = x^2+(a+b)x+ab`