Determine if the polynomial \(4x^4 - 10x^3 + 4x^2 - 10x + 4\) can be factored by the binomial \(2x-1\) using synthetic division.

Step 1 ：Step 1: Set up the synthetic division. Write the coefficients of the polynomial at the top of your synthetic division symbol and the number that makes the binomial equal to zero on the outside. In this case, the number is \(\frac{1}{2}\) because \(2x-1=0\) when \(x=\frac{1}{2}\).

Step 2 ：Step 2: Carry the first coefficient (4) straight down and then multiply it by \(\frac{1}{2}\) (which you get from the binomial \(2x-1\)), and write the result under the next coefficient. Repeat this process for all coefficients.

Step 3 ：Step 3: Add down the columns. If the last number you get is zero, then \(2x-1\) is a factor of the polynomial.