How to factor $2x^3-5x-3$?

Question

How can we factor $2x^3-5x-3$?

I couldn't do any work in this expression, please help.

Answer 1

Look this factorization

$$ 2x^3-5x-3=(x+1) (2 x^2-2 x-3)$$

or

$$2x^3-5x-3=-\frac12 (-2 x+\sqrt{7}+1) (x+1) (2 x+\sqrt{7}-1)$$

Answer 2

the best way to factor polynomials greater than degree two is through the use of Polynomial Long Division. Via inspection it appears that one root is $x = -1$, and a quick check verifies this: $2(-1)^{3} - 5(-1) - 3 = -2 + 5 - 3 = 0$. It should be pretty easy to proceed from there

Answer 3

You can add subtract terms to get common $x+1$. $$2x^3-5x-3=2x^3+2x^2-2x^2-5x-3$$ I added and subtracted $2x^2$to get $x+1$ common. $$2x^2(x+1)-2x^2-2x+2x-5x-3=2x^2(x+1)-2x(x+1)-3x-3$$ Now,I added and subtracted $2x$. $$2x^2(x+1)-2x(x+1)-3(x+1)=(x+1)(2x^2-2x-3)$$ At last, I got $x+1$ common.