To factor a trinomial, first we should factor out the GCF, or greatest common factor, shared by all of the coefficients and constants. The greatest common factor of -3, -21, and -30 is -3, therefore, this is the number we must factor out first.
When we factor out the GCF of -3, we get: -3(q^2 + 7q + 10)
Next, we must look for two numbers that will serve as coefficients for the variables in factored form. These two numbers must add to 7 (the middle term) and multiply to 10 (the constant or last term). The two numbers that satisfy these parameters are 5 and 2.
Therefore, we must use these numbers to create factors of the innermost factor that we have left, to get:
-3(q+5)(q+2)
The above expression is your final answer, because you cannot factor any more. And remember: you can always check to make sure that your factoring is correct by multiplying out the factors and making sure you get your original trinomial.
