Question

How do you factor the trinomial `x^2 - 7x + 12`?

Answer 1

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

Here's how I did it:

Explanation:

Two factor a trinomial in form `ax^2 + bx + c`, you must find two numbers that:
`color(red)ax^2 + color(magenta)bx^2+color(blue)c`

• Multiply up to `color(red)acolor(blue)c`
• Add up to `color(magenta)b`

In this question, that means the two numbers must:

• Multiply up to `(color(red)1)(color(blue)12) = 12`
• Add up to `color(magenta)(-7)`

These two numbers are `-3` and `-4`:
`-3 * -4 = 12`
`-3 -4 = -7`

So now we put them into factored form:
`(x-3)(x-4)`

Hope this helps!

Answer 2

The factors always multiply to C (12) and add to Bx (7x).
In this case, the answer is (x-4)(x-3) because multiplying two negatives equal a positive and adding two negatives are still negative.