Factor completely, or state that the trinomial is prime.
3y^3 + 15y^2 + 18y
= (y/3)(y^2+5y+6)
= (y/3)(y+2)(y+3)
3y(y^2 +5y + 6) = 3y(y+2)(y+3)
To factor the given trinomial, 3y^3 + 15y^2 + 18y, we need to look for a common factor that can be factored out from each term. In this case, the common factor is 3y, as it can be factored out from each term.
Factoring out 3y from each term, we get:
3y(y^2 + 5y + 6)
Now, we need to factor the quadratic expression in the parentheses, which is y^2 + 5y + 6. This quadratic trinomial can be factored into two binomials. We need to find two numbers that multiply to give 6 and add up to 5.
The numbers 2 and 3 satisfy these conditions because 2 * 3 = 6, and 2 + 3 = 5.
Therefore, we can rewrite the quadratic trinomial as:
3y(y + 2)(y + 3)
So, the factored form of the given trinomial is 3y(y + 2)(y + 3).