Factoring the cubic equation y=2x^3 +2 ?

To factor the cubic equation y=2x^3 +2, we first need to factor out the common factor of 2:

y = 2(x^3 + 1)

Now, we can see that the expression inside the parentheses is a sum of cubes, which can be factored using the formula a^3 + b^3 = (a + b)(a^2 - ab + b^2):

y = 2(x + 1)(x^2 - x + 1)

Therefore, the factored form of the cubic equation y=2x^3 +2 is y = 2(x + 1)(x^2 - x + 1).

$$y=2x^3 - 2$$

$$y+2=2x^3$$

$$(y+2)=(2x)3$$

$$(y+2)^{1/3}=2x$$

$$(y+2)^{1/3}\frac{1}{2}=x$$

$$x=\frac{1}{2}(y+2)^{1/3}$$