Question

Factoring trinomials,help?

Answer 1

Hey there!

When factoring trinomials, we're usually looking at the trinomial in the format of:

ax^2 + bx + c

In order to factor these, we have to use a different method than when a<1. When a is less than one, we can simply figure out the factors that add to the middle term and multiply to the last, but here we have to do a little something different.

The first step is to factor out the GCD of these terms. As you can see, there isn't one, as 13 is prime.

The next step is to multiply a by c:

6(6) = 36

Next, we have to, using the pattern of trinomials(the two binomials would have factors that add to the middle term and multiply to the last), we have to find factors of 36 that multiply to 36 and add to -13. When we do this step, we can disregard the last term for now. Let's list factors of 36:

36 =
18, 2 = 20
9,4 = 13
-9, -4 = 13
 
 -9 and -4 work for this. We can now write them as x terms and factor by grouping:

6m^2 - 4m - 9m + 6   (don't forget that last term)

For the left side, factor out a 2m:

2m(3m - 2)

For the right side, factor out a -3:

2m(m-2) - 3(m-2)

Now that we have our common factor of m-2, we can write them as a product of 2 binomials:

(2m-3)(m-2)

Hope this helps!