Factor 3x^3 + 9x^2 - 3x - 9

3x^3 + 9x^2 - 3x - 9

3 (x^3 + 3x^2- x - 3)
3 ( x+3x^2) ( -x - 3)
3 {x( 1 + 3x) -1 (x -1)

This is a far I have gotten. Can someone please help me through the rest of the answer?

Thank You

no

(e_e)

take out a common factor, then use grouping ...

3x^3 + 9x^2 - 3x - 9
= 3(x^3 + 3x^2 - x - 3)
= 3( x^2(x + 3) - (x + 3)
= 3(x+3)(x^2 - 1)
= 3(x+3)(x-1)(x+1)

Thank you

Certainly! You're on the right track so far. Let's continue factoring the expression 3x^3 + 9x^2 - 3x - 9.

We have reached the expression 3 (x^3 + 3x^2 - x - 3). Now, let's focus on factoring the part inside the parentheses: x^3 + 3x^2 - x - 3.

To factor this, we can start by grouping terms with common factors. Let's group the first two terms (x^3 + 3x^2) and the last two terms (-x - 3):

(x^3 + 3x^2) - (x + 3)

Now, we can factor out the greatest common factor from each group separately.

From the first group (x^3 + 3x^2), we can factor out an x^2, giving us x^2(x + 3).

From the second group (-x - 3), we can factor out a -1, giving us -1(x + 3).

Putting it all together, we have x^2(x + 3) - 1(x + 3).

Now, notice that we have a common factor of (x + 3) in both terms. We can factor out this common factor, resulting in:

(x + 3)(x^2 - 1).

Finally, we can further simplify the expression x^2 - 1 by recognizing that it is a difference of squares:

(x + 3)(x - 1)(x + 1).

Therefore, the fully factored form of 3x^3 + 9x^2 - 3x - 9 is:

3(x + 3)(x - 1)(x + 1).

I hope this helps! Let me know if you have any further questions.