Ok, I hope there’s a math wiz out there who can help me. I have to factor: [tex]f (x)=3x^4-8x^3-5x^2+16x-5[/tex] Just from looking at it, you know that possible values for x are: ±1, ±5/3, ±1/3, ±5 However, if you plug in these real numbers, none of them work, therefore meaning that x is an irrational number and is complex/imaginary. Note that I’m using synthetic division to solve the equation. So, my question would be, how do I solve for irrational numbers? The quadratic equation will probably be required, but I’m still not sure how to get the final answer. I’d appreciate an answer along with the steps to solving the problem. This is for extra credit in my class, so we have not been taught yet, and I’d like to get extra credit. I realize I haven't given much time for this equation to be solved, but Id appreciate an answer by Monday.