Trinomials: factoring when leading coeff. not 1: 4x^2+6x+9

[Tiger]

I am having a problem figuring out trinomials when there is a number added to the first term. I understand the second sign determines both signs below and the sign on the left determines what they will be. I also believe I figured out the first term. The problem is there are five different options with this problem. Is there a fast way to determine if you are on the right track without having to FOIL all five options?

4x^2 + 6x + 9

(x + 1) (4x + 9)
(x + 9) (4x + 1)
(x + 3) (4x + 3)
(2x + 1) (2x + 9)
(2x + 3) (2x + 3)

[stapel_eliz]

I am having a problem figuring out trinomials when there is a number added to the first term.

To learn a much easier method, try here.

Once you've learned that method, note that (4)(+9) = +36. Since the 36 is positive, then the factors you're looking for both have the same sign. Since the middle term's coefficient is +6, the factors have to be positive and add to 6.

The factor pairs for 36 are 1 and 36, 2 and 18, 3 and 12, 4 and 9, and 6 and 6. No pair adds to 6! This tells you that the quadratic is not factorable; it is "prime".

[Tiger]

Thank you for your help. The box method is much faster.