How do I factor trinomials?

Reverse foil is a good method, for example I recognize that (x-a)(a-b) would give me a polynomial mirroring that of the problem, and solve the values of a and b to get...

Answer: (x+7)(x-2)!!!

Here's the way I learned it:

1) Rewrite the trinomial with the largest powers first

x^2 + 5x - 14

2) Multiply the first term and the last term together (don't include the x)

1 times -14 = -14

3) Now find a two numbers that will multiply to the product of the outside two terms (-14) and add to the middle term (5).

7 and -2 because -2 times 7 = -14 and 7 + -2 = 5

4) Now take the square root of the first term and add it to the first number you found and multiply that by the square root of the first term plus the second number you found.

(x + 7)(x - 2)

And that's your answer.

First of all, put it in order of powers of x

x^2 + 5x -14

Then open 2 brackets and write x on the left of each bracket

(x____)*(x____)

Now what 2 numbers multiply together to give -14, all these multiply to give -14:

(a) -1*14

(b) 1*-14

(c) -2*7

(d) 2*-7

Which 2 numbers from the above list add to give 5 (because its 5x):

(a) -1+14=13

(b) 1-14=-13

(c) -2+7=5-------->this one

(d) 2-7=-5

so our choice will be (c)

so the answer is:

(x-2)(x+7)