The expression you provided is:

\[
3x^2 + 3x - 6
\]

We can simplify it by factoring out the greatest common factor (GCF), which is 3:

\[
3(x^2 + x - 2)
\]

Next, we can factor the quadratic expression inside the parentheses:

\[
x^2 + x - 2
\]

To factor \(x^2 + x - 2\), we look for two numbers that multiply to \(-2\) and add up to \(1\). The factors are \(2\) and \(-1\), so the factored form is:

\[
(x + 2)(x - 1)
\]

Thus, the fully factored form of the expression is:

\[
3(x + 2)(x - 1)
\]

Would you like further details or any clarification?

Here are 5 related questions for practice:
1. How would you factor \(4x^2 + 4x - 8\)?
2. Can you solve the equation \(3x^2 + 3x - 6 = 0\)?
3. How would you expand the expression \(3(x + 2)(x - 1)\)?
4. What are the solutions to \(x^2 + x - 2 = 0\)?
5. How does factoring help in solving quadratic equations?

**Tip:** Always check for a common factor before factoring quadratics!

Discover how to factor the quadratic expression 3x^2 + 3x - 6 by using the greatest common factor and factoring techniques. This solution explains each step in detail, helping students understand algebraic factoring concepts. Ideal for Grades 8-10.

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