Here is one of my equations - "factor the given trinomial a2+3a+2

I am completely lost Here is one of my equations

are you in algebra 2?

yes

No problem! Factoring a trinomial is a common algebraic skill. To factor the given trinomial, which in this case is a² + 3a + 2, you can follow these steps:

Step 1: Look for two numbers that multiply to give you the constant term (in this case, 2) and add up to the coefficient of the middle term (in this case, 3).

So, in the given trinomial a² + 3a + 2, we need to find two numbers that multiply to give 2 and add up to 3.

Step 2: The numbers that satisfy these conditions are 1 and 2. Why? Because 1 multiplied by 2 equals 2, and 1 plus 2 equals 3.

Step 3: Now we use the numbers we found in the previous step to rewrite the middle term (3a) of the trinomial. We replace the 3a with the sum of the two numbers (1 and 2), and we rewrite it as 1a + 2a.

So, the trinomial a² + 3a + 2 can be rewritten as a² + 1a + 2a + 2.

Step 4: Group the terms. We group the first two terms and the last two terms together.

So, a² + 1a can be grouped together, and 2a + 2 can be grouped together.

Step 5: Factor out any common factors from each group. In the first group, we can factor out an "a". In the second group, we can factor out a "2".

So, we get a(a + 1) + 2(a + 1).

Step 6: Notice that now we have a common binomial factor, which is (a + 1). We can factor it out.

Therefore, the fully factored form of the given trinomial a² + 3a + 2 is (a + 1)(a + 2).

And that's it! We have successfully factored the trinomial a² + 3a + 2.