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!

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- Sep 27th 2007, 03:39 PMvpereraFactoring polynomials
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! - Sep 27th 2007, 06:18 PMSnipedYou
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) - Sep 28th 2007, 04:54 AMtopsquark
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-Dan