Explanation:
To factor the quadratic expression 3x^2 + 9x - 3 completely, we can start by factoring out the greatest common factor (GCF) of all the terms. The GCF of 3x^2, 9x, and -3 is 3. Factoring out the GCF, we get:
3x^2 + 9x - 3 = 3(x^2 + 3x - 1)
Now we need to factor the quadratic expression inside the parentheses. Since the coefficient of x^2 is 1, we can look for two numbers that multiply to -1 (the constant term) and add to 3 (the coefficient of x). These two numbers are -1 and 4. So we can write:
x^2 + 3x - 1 = (x - 1)(x + 4)
Substituting this back into our original expression, we get:
3x^2 + 9x - 3 = 3(x^2 + 3x - 1) = 3(x - 1)(x + 4)
So the complete factorization of 3x^2 + 9x - 3 is 3(x - 1)(x + 4).