First multiply 3 and 4 to get 12. Now, we must get two numbers that multiply to 12, but also add to -8. The answer is -6 and 2.
Now rewrite this expression as “3x^2-6x+2x+4.
Now, group together each set of two terms and find the GCF of each. The GCF of 3x^2 and -6x is -3x. The GCF of 2x and 4 is 2.
Now, divide each group by the GCFs and place them next to each other. You should get -3x(x+2)+2(x+2). We know this is correct because the parentheses match.
Now, rewrite the duplicate factors as one, and group together what is outside the parentheses. The final answer is...
(-3x+2)(x+2).
To check, you can double distribute (FOIL) to see if it matches the original expression.