find the remainder when dividing the polynomiak 4x^3 -2x +7 by x-1

To find the remainder when dividing the polynomial 4x^3 -2x +7 by x-1, we can use polynomial division or synthetic division. Here, we'll use synthetic division.

Step 1: Write down the coefficients of the polynomial. For 4x^3 -2x +7, the coefficients are 4, 0 (for x^2, which is missing in the polynomial), -2, and 7.

Step 2: Write down the root of the divisor. The root of x-1 is 1.

Step 3: Set up the synthetic division. Draw a line, write the root on the left, and the coefficients on the right.

        1 | 4  0  -2  7

Step 4: Bring down the first coefficient (4 in this case).

        1 | 4  0  -2  7
            ------------
              4

Step 5: Multiply the root by the number you just wrote down, and write the result under the next coefficient. Then add the numbers in that column and write the result below.

        1 | 4  0  -2  7
            ------------
              4  4

Step