Find all of the roots of the equation y = 3x^3 - 12x
Step 1: Remove the most obvious factor, in this case 3x. y = 3x (x2 - 4) Step 2: Realize (x2 - 4) is the product of two squares and can undergo completing the square to produce two factors. y = 3x (x-2) (x+2) Step 3: Set each factor to equal 0 then rearrange to find the x value, as when the curve crosses the x-axis the value for the y component will be 0 and therefore at each root one of the factors will be equal to 0. 3x = 0, so x = 0. x-2 = 0, so x = 2. x+2 = 0, so x = -2. Therefore the roots are at (-2,0), (0,0) and (2,0)
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