First you graph it using a graphing calculator, you look at the table of values to find out one point in which y= 0. The first one that comes up is when x=1. If you don't have a graphing calculator you can use trial and error by inputing some numbers into x until you get y= 0.
Once you have an x value which makes y=0, you can start factorizing it. you divide 6x3 +4x2 -6x - 4 into (x-1) which is when y =0 to get 6x2+10x+4
This can be used to write the polynomial as (x-1)(6x2 +10x+4) you then factorize the second bracket, 6x2 +10x+4. you can take the 2 outside to give you 2(3x2 +5x+2) you can factorize this to become 2(3x+2)(x+1)
Now you just substitute your factorized second bracket into your unfactorized second bracket to give you 2(3x+2)(x+1)(x-1).
The graph of a quadratic function y = ax² is a VERTICAL parabola open upward or downward depending whether a (the coefficient of x) is positive or negative
The graph y² = ax or y = √ax is a HORIZONTAL parabola open to the right or to the left depending whether a (the coefficient of x) is positive or negative
