Question

How do you factor the trinomial `x^2 + 13x + 42`?

Answer 1

`(x+6)(x+7)`

Explanation:

When we look at the trinomial, there is no number (coefficient) in front of `x^2`, so we know that it is a simple trinomial. All you have to do in a simple trinomial is to find two numbers that not only add up to the `b` term, but multiply to the `c` term.

In this trinomial, the `b` term is `13`, so you need to find two numbers that add up to `13`. That could be

• `5 and 8`
• `6 and 7`
• `11 and 2`

and so on. But these two numbers need to multiply to get the `c` term. In this case, it's `42`. So what two numbers add up to `13` and multiply to `42`? The answer is `6` and `7`.

`6+7=13 and 6xx7=42`

After this, all you need to do is put this in binomial form, so take an `x`, and add your first number

`(x+6)`

Then multiply this by another `x +` the second number

`(x+7)`

And there you have the answer:

`(x+6)(x+7)`

If you're ever unsure of your answer, try to expand and simplify the answer. If you go back and the expanded/simplified version is the same trinomial you started with, that means you did it right.