I need help with factoring trinomials completely. My teacher's example is:

2x^2-12x+18
2(x^2-6x+9)
2(x-3)(x-3)

I need help with:
6x^2-26x-20

I just can't get this stuff so if you can please help me I'd greatly appreciate it.

6x^2-26x-20 =

2(3x^2 - 13 x - 10) =

2(3 x + 2)(x - 5)

Wow, thanks, now there is one more type I am stuck on and it is:

6y^2-24

6(y^2-4)

6(y-2)(y+2)...

Incredible. Thanks you two, you really helped me.

Of course, I'd be happy to help you with factoring trinomials! Let's go through the steps together for factoring the trinomial 6x^2 - 26x - 20.

Step 1: Make sure the trinomial is in the form ax^2 + bx + c, where a, b, and c are integers.
In this case, the trinomial is already in the required form: 6x^2 - 26x - 20.

Step 2: Multiply the coefficient of the leading term (a) by the constant term (c).
In this case, a = 6 and c = -20, so the product is 6 * (-20) = -120.

Step 3: Find two integers whose product is equal to the product obtained in Step 2, and whose sum is equal to the coefficient of the middle term (b).
In this case, the product is -120. We need to find two numbers whose product is -120 and whose sum is -26. After some trial and error, we find that -30 and 4 satisfy these conditions.

Step 4: Rewrite the middle term (bx) using the two numbers found in Step 3.
Replace -26x with -30x + 4x in the trinomial:
6x^2 - 30x + 4x - 20

Step 5: Group the terms in pairs and factor out the greatest common factor (GCF) from each pair.
Taking the GCF from the first pair and the second pair:
2x(3x - 15) + 4(3x - 5)

Step 6: Check if there is a common binomial factor. If so, factor it out.
In this case, you can factor out a common binomial factor of (3x - 5):
(3x - 5)(2x + 4)

So the completely factored form of 6x^2 - 26x - 20 is: (3x - 5)(2x + 4).

Remember, factoring trinomials may require some practice, so don't hesitate to try more examples to gain more familiarity with the process.