Use synthetic division to find the quotient and remainder.
(r^2-2r+2), (r-1)
sort of hard to line numbers up nicely in this format, the .... represents spaces
1 | 1 -2 +2
......... 1 ..-1
..... 1 -1 1
so (r^2 - 2r + 2) ÷ (r-1) = r-1 + 1/(r-1)
or
r-1 with a remainder of 1
for a nice online worksheet that does proper formatting and shows all the details, try calc101.com and click on the "long division" button.
To use synthetic division to find the quotient and remainder, follow these steps:
1. Write the dividend and divisor in the standard form, with descending powers of the variable. In this case, the dividend is r^2 - 2r + 2, and the divisor is r - 1.
2. Set up the synthetic division table. Draw a horizontal line underneath the terms of the dividend, and write the divisor to the left of the line. In this case, the divisor is r - 1, so you write 1 to the left of the line.
1
3. Bring down the coefficient of the highest power of the dividend, which is 1 in this case. Write it below the line.
1
1
4. Multiply the number below the line (1) by the divisor (1) and write the result above the line and to the right of the next coefficient of the dividend. In this case, 1 * 1 = 1, so we write it below the line and to the right of -2.
1
-1 1
5. Add the numbers diagonally. In this case, -2 + 1 = -1. Write the result below the line to the right of the previous result.
1
-1 1
-----
-1
6. Multiply the number below the line (-1) by the divisor (1) and write the result above the line and to the right of the next coefficient of the dividend. In this case, -1 * 1 = -1, so we write it below the line and to the right of 2.
1
-1 1
-----
-1 -1
7. Add the numbers diagonally. In this case, 2 + (-1) = 1. Write the result below the line to the right of the previous result.
1
-1 1
-----
-1 -1
1
8. The numbers above the line represent the coefficients of the quotient, starting from the highest power and going to the lowest power. Therefore, the quotient is r - 1.
9. The number below the line is the remainder. In this case, the remainder is 1.
So, the quotient is r - 1 and the remainder is 1.