Final answer:
To divide 2x^(3)-x^(2)+10x+5 by 2x-1, we can use polynomial long division. The result will be x^(2)+5.5 remainder 10.5.
Step-by-step explanation:
To find the result when 2x^(3)-x^(2)+10x+5 is divided by 2x-1, we can use polynomial long division.
Start by dividing the first term, 2x^(3), by 2x. This gives us x^(2).
Multiply (2x-1) by x^(2) to get 2x^(3)-x^(2).
Subtract 2x^(3)-x^(2) from 2x^(3)-x^(2)+10x+5 to get 11x+5.
Repeat the process with the new dividend (11x+5). Divide 11x by 2x to get 5.5.
Multiply (2x-1) by 5.5 to get 11x-5.5.
Subtract 11x-5.5 from 11x+5 to get 10.5.
Finally, divide 10.5 by 2x-1 to get the remainder.