Factor completely this trinomial
3y^3+15y^2+18y
First factor out y.
y(3y^2+15y+18)
What multiplies to give you 18 and adds to give you 15?
y(3y+6)(y+3)
I hope this helps.
To factor the trinomial 3y^3 + 15y^2 + 18y completely, we can start by factoring out the greatest common factor (GCF) from all three terms. In this case, the GCF is 3y.
Step 1: Factor out the GCF:
3y( y^2 + 5y + 6)
Now, we have a quadratic trinomial inside the parentheses (y^2 + 5y + 6). To factor this quadratic trinomial further, we need to find two numbers that multiply to give 6 (the constant term) and add up to give 5 (the coefficient of the middle term).
Step 2: Factor the quadratic trinomial:
3y( y + 3)(y + 2)
Thus, the completely factored form of the given trinomial is 3y(y + 3)(y + 2).