Question

Solve for y: y^3+5y^2−9y−45=0

Answer 1

For this, I will be factoring by grouping to solve for y.

Firstly, factor y^3 + 5y^2 and -9y - 45 separately, Make sure that they have the same quantity on the inside:

$y^2(y+5)-9(y+5)=0$

Now you can rewrite it as $(y^2-9)(y+5)=0$ . However we are not finished factoring.

Now with y^2 - 9, we will apply the difference of squares rule, which is $x^2-y^2=(x+y)(x-y)$ . Apply it as such:

$(y+3)(y-3)(y+5)=0$

Now that it is completely factored, we can apply the Zero Product Property and solve for y:

$y+3=0\\y=-3\\\\y-3=0\\y=3\\\\y+5=0\\y=-5$

In short, y = -5, -3, and 3.