Answer:
3(x - 1)(x + 2)
Step-by-step explanation:
Factor 3x^2 + 3x - 6
Step 1: Factor out a common factor from all terms if possible.
All terms have a common factor of 3. We start by factoring out the 3.
3x^2 + 3x - 6 =
= 3(x^2 + x - 2)
Step 2: We now need to deal with factoring x^2 + x - 2.
It is a trinomial of the form x^2 + ax + b, where the coefficient of x^2 is 1. To factor it, we need 2 numbers whose product is b and whose sum is a. In our case, we have x^2 + x - 2. We need two numbers whose product is -2 and whose sum is 1.
Pairs of numbers with product -2:
-2 and 1 since -2 * 1 = -2
-1 and 2 since -1 * 2 = -2
Now we add the two numbers in each line above.
-2 + 1 = -1 The sum is -1, but we need a sum of 1, so this is not it.
-1 + 2 = 1 Here we do get the sum of 1 that we need, so this pair of numbers is what we need.
The two numbers we need for factoring are -1 and 2.
Now we start the next step.
The factored trinomial will have this form.
= 3(x )(x )
All we need to do now is place each of the numbers in one of the blanks.
= 3(x - 1)(x + 2)
Answer: 3(x - 1)(x + 2)
