Hello, I need help factoring the following: 2x^3 - 5x - 3
I've gotten as far as using the payback method to get: x^3 - 5x - 6 but I can't seem to go beyond that.
Help is appreciated, thanks!
Try doing synthetic division. So we have the polynomial $\displaystyle 2x^{3}-5x-3=0$ Lets try some easy numbers, like $\displaystyle -1, 0, 1$ to see if they satisfy the polynomial. By plugging in these numbers we can see that $\displaystyle -1$ is a factor meaning that $\displaystyle (x+1)$ satisfies the polynomial. Now we can do synthetic division: (Make sure to put a 0 for all variables that are missing)
-1| 2 0 -5 -3
0 -2 2 3
2 -2 -3 0
So now we can see that $\displaystyle (x+1)(2x^{2}-2x-3)$ are factors. Simply do the quadratic equation from here. (Sorry if some of the steps were unclear, I am not that great at explaining)