What is the remainder when x2 – 5x + 7 is divided by x + 1?

To find the remainder when x^2 - 5x + 7 is divided 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 dividend (x^2 - 5x + 7), which are 1, -5, and 7.

Step 2: Write down the root of the divisor (x + 1), which is -1.

Step 3: Set up the synthetic division table:

-1 |  1  -5   7
    |     1   4
---------------
    |  1  -4   11

Step 4: The numbers on the bottom row are the coefficients of the quotient plus the remainder. The last number, 11, is the remainder.

So, the remainder when x^2 - 5x + 7 is divided by x + 1 is 11.