How to find the factor of a trinomial?

I can tell you about the 'ac' method of factoring trinomials by way of an example:-

Factor   3x^2 - 4x - 15

first multiply the first number by the last  That is 3 * -15   = -45

Now we need to find  2 factors of -45 which will when added give - 4 ( the coefficient of x)

-9 and = 5  look like the  ones so we write

3x^2 - 9x + 5x - 15

 Now  factor this by grouping:-

= 3x(x - 3) + 5(x - 3)

x - 3 is common to the 2 parts so we have:-

(3x + 5)(x - 3)  < These are your  factors

Any trinomial can be factored in this way.

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