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!
the payback method? what's that? whatever it is, it is incorrect.
first try the factors of 3 into the formula to see if we can get zero. we realize that plugging in $\displaystyle x = -1$ gives zero. thus $\displaystyle x = -1$ is a root of the cubic, and so $\displaystyle (x + 1)$ is a factor, by the factor theorem.
by way of polynomial long division or synthetic division, we find that:
$\displaystyle \left( 2x^3 - 5x - 3 \right) \div (x + 1) = 2x^2 - 2x - 3$
thus, $\displaystyle 2x^3 - 5x - 3 = (x + 1) \left( 2x^2 - 2x - 3 \right)$
and you can continue to factor the quadratic, but only if you really want to, it will be tedious to work out, and it won't look very nice when you're done, if you decide to