Question

factor the following trinomial.

\\y^4 - 15y^3 + 54y^2\\

\\y^4 - 15y^3 + 54y^2 = \text{ (factor completely.)}\\

Explanation:

Factor out the greatest common factor

$$ y^4 - 15y^3 + 54y^2 = y^2(y^2 - 15y + 54) $$

Factor the remaining quadratic trinomial

$$ y^2 - 15y + 54 = (y - 6)(y - 9) $$

Combine the factored components

$$ y^4 - 15y^3 + 54y^2 = y^2(y - 6)(y - 9) $$

Answer:

Factor the following trinomial.

\(y^4 - 15y^3 + 54y^2 =\) <blank>\(y^2(y - 6)(y - 9)\)</blank> (Factor completely.)