# Factoring polynomials

• Sep 27th 2007, 03:39 PM
vperera
Factoring 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 PM
SnipedYou
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 AM
topsquark
Quote:

Originally Posted by vperera
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!

Please don't double post. See rule #1 here.

-Dan