The correct quotient for x^3 - 3x^2 + 4 divided by x + 1 is x^2 - 2x + 2 with a remainder of 2. Therefore, the error in the student's setup occurred in the last term of the quotient, where the correct value is 1, not 2.
In synthetic division, it's crucial to set up the division correctly to ensure accurate results. Let's analyze the student's setup for dividing x^3 - 3x^2 + 4 by x + 1.
The synthetic division setup involves arranging the coefficients of the dividend (in descending order) and the divisor. The process then iteratively combines these coefficients to find the quotient. For this specific case:
Coefficients of Dividend: 1 -3 0 4
The student appears to have correctly listed the coefficients of the dividend x^3 - 3x^2 + 4.
Divisor:
x + 1 implies the divisor coefficients are 1 and 1.
Now, let's perform synthetic division:
-1 | 1 -3 0 4
| -1 2 -2
The synthetic division process involves multiplying the divisor by the number at the top of the dividend column and subtracting it from the next column. However, it seems there might be an error in the last term of the quotient. The student subtracted 2 instead of 1, possibly overlooking the sign change.