College Algebra (10th Edition)

$y^2(y+5)(y+6)$
Factor out $y^2$ to obtain: $=y^2(y^2+11y+30)$ RECALL: A trinomial of the form $x^2+bx+c$ can be factored if there are integers $d$ and $e$ such that $c=de$ and $b=d+e$. The trinomial's factored form will be: $x^2+bx+c=(x+d)(x+e)$ The trinomial above has $b=11$ and $c=30$. Note that $30=5(6)$ and $11= 5+6$. This means that $d=5$ and $e=6$ Thus, the factored form of the trinomial is: $(y+5)(y+6)$ Therefore, the completely factored form of the given expression is: $y^2(y+5)(y+6)$