Final answer:
The function -2x³ - 4x² + 30x can be factored by first taking out the greatest common factor, resulting in y = -2x(x² + 2x - 15), which further factors to y = -2x(x + 5)(x - 3).
Step-by-step explanation:
The function given is y = -2x³ - 4x² + 30x. To write this function in factored form, we first factor out the greatest common factor, which in this case is -2x. So we get y = -2x(x² + 2x - 15). The quadratic equation x² + 2x - 15 can then be factored into (x + 5)(x - 3), since 5 and -3 are the numbers that add up to 2 and multiply to -15. Our final factored form of the function is y = -2x(x + 5)(x - 3).