Complete the factoring.
3x^3+9x^2+6x
3x^3 + 9x^2 + 6x
3x(x^2 + 3x + 2)
3x(x+1)(x+2)
To factor the expression 3x^3 + 9x^2 + 6x, we look for common factors that can be factored out from each term. In this case, the common factor is 3x, which we can factor out:
3x^3 + 9x^2 + 6x
= 3x(x^2 + 3x + 2)
Now, we need to factor the expression (x^2 + 3x + 2) further. To do this, we look for two numbers whose product is equal to the product of the coefficient of x^2 (which is 1) and the constant term (which is 2). Additionally, we want these two numbers to sum to the coefficient of x (which is 3).
The numbers 1 and 2 fit these requirements, so we can rewrite the expression as:
3x(x^2 + 3x + 2)
= 3x(x + 1)(x + 2)
Therefore, the completely factored expression is 3x(x + 1)(x + 2).