## No worries! Factoring can be a bit tricky, but with practice, it becomes easier.

Let's take a closer look at your first problem:

2(2n² - 10n + 12)

To factor the trinomial 2n² - 10n + 12, we need to find two numbers that multiply to give the constant term (12) and add up to the coefficient of the linear term (-10).

In this case, we are looking for two numbers that multiply to give 12 and add up to -10. One way to determine these numbers is by listing all possible factor pairs of 12:

1 and 12

2 and 6

3 and 4

Now, let's see if any of these pairs add up to -10.

1 + 12 = 13

2 + 6 = 8

3 + 4 = 7

None of these pairs adds up to -10. Therefore, we cannot factor the trinomial using integer factors.

However, there is another technique we can use called factoring by grouping. Here's how it works:

1. Split the middle term, -10n, into two terms such that their coefficients multiply to give the product of the coefficient of the square term (2) and the constant term (12). In this case, that product is 24.

2. Rewrite the trinomial, grouping the terms properly:

2n² - 10n + 12 = 2n² - 4n - 6n + 12

3. Now, factor by grouping:

2n² - 4n - 6n + 12 = 2n(n - 2) - 6(n - 2)

4. Notice that we now have a common binomial term, (n - 2). We can factor it out:

2n(n - 2) - 6(n - 2) = (n - 2)(2n - 6)

So, the factored form of the trinomial 2(2n² - 10n + 12) is (n - 2)(2n - 6).

I hope this helps! Let me know if there's anything else you need assistance with.