Factor the polynomial completely, if possible. If the expression cannot be factored, enter the expression as is. \[ 40 x^{3}-68 x^{2}-44 x \]

To factor the polynomial \( 40 x^{3}-68 x^{2}-44 x \), we can start by finding the greatest common factor (GCF) of the coefficients. The GCF of \( 40, -68, \) and \( -44 \) is \( 4 \). Factoring out \( 4x \) gives us: \[ 4x(10x^2 - 17x - 11) \] Next, we need to factor the quadratic \( 10x^2 - 17x - 11 \). This can be done by looking for two numbers that multiply to \( 10 \times -11 = -110 \) and add to \( -17 \). These two numbers are \( -22 \) and \( 5 \). Now, we can rewrite the quadratic: \[ 10x^2 - 22x + 5x - 11 \] Grouping terms gives us: \[ (10x^2 - 22x) + (5x - 11) \] \[ = 2x(5x - 11) + 1(5x - 11) \] \[ = (2x + 1)(5x - 11) \] Putting it all together, we have: \[ 4x(2x + 1)(5x - 11) \] So, the factored form of the polynomial \( 40 x^{3}-68 x^{2}-44 x \) is: \[ \boxed{4x(2x + 1)(5x - 11)} \]