Final answer:
To find the remainder when f(x)=2x⁴-1 is divided by x-1, use synthetic division.
Step-by-step explanation:
To find the remainder when f(x)=2x⁴-1 is divided by x-1, we can use synthetic division. Synthetic division is a shortcut method used to divide a polynomial by a linear factor. The remainder will be the value obtained in the last step of synthetic division.
Step 1: Set up the synthetic division table. Place the divisor (x-1) in the first row and write the coefficients of f(x) in the second row.
Step 2: Bring down the first coefficient, which is 2. Multiply it by the divisor and write the product in the next row. Add the values in that row and write the sum in the next row.
Step 3: Repeat step 2 for the next coefficient until all the coefficients have been used.
Step 4: The remainder is the value obtained in the last row of the synthetic division table. In this case, the remainder is 1.