Question

Write the function in factored form. Check by multiplication. y=-2x^3-4x^2+30xy= _______ (Factor completely.)

Answer 1

Let's start by factoring the term -2x in the expression:

`\begin{gathered} y=-2x^3-4x^2+30x\\ \\ y=-2x(x^2+2x-15) \end{gathered}`

Now, to factor the quadratic expression, let's first calculate its zeros using the quadratic formula:

`\begin{gathered} a=1.b=2,c=-15\\ \\ x=(-b±√(b^2-4ac))/(2a)\\ \\ x=(-2±√(4+60))/(2)\\ \\ x_1=(-2+8)/(2)=3\\ \\ x_2=(-2-8)/(2)=-5 \end{gathered}`

The factored form of a quadratic equation is:

`\begin{gathered} a(x-x_1)(x-x_2)\\ \\ =(x-3)(x+5) \end{gathered}`

Therefore, after factoring y completely, we have:

`y=-2x(x-3)(x+5)`