Let's start by factoring the term -2x in the expression:
[tex]\begin{gathered} y=-2x^3-4x^2+30x\\ \\ y=-2x(x^2+2x-15) \end{gathered}[/tex]
Now, to factor the quadratic expression, let's first calculate its zeros using the quadratic formula:
[tex]\begin{gathered} a=1.b=2,c=-15\\ \\ x=\frac{-b±\sqrt{b^2-4ac}}{2a}\\ \\ x=\frac{-2±\sqrt{4+60}}{2}\\ \\ x_1=\frac{-2+8}{2}=3\\ \\ x_2=\frac{-2-8}{2}=-5 \end{gathered}[/tex]
The factored form of a quadratic equation is:
[tex]\begin{gathered} a(x-x_1)(x-x_2)\\ \\ =(x-3)(x+5) \end{gathered}[/tex]
Therefore, after factoring y completely, we have:
[tex]y=-2x(x-3)(x+5)[/tex]
