x2 – 5x + 7 is divided by x + 1?

To divide the quadratic equation "x^2 - 5x + 7" by "x + 1", we can use polynomial long division or synthetic division. Here, we'll use polynomial long division.

Step 1: Set up the long division. Write "x^2 - 5x + 7" inside the division symbol and "x + 1" outside.

Step 2: Divide the first term of the dividend (x^2) by the first term of the divisor (x) to get the first term of the quotient (x).

Step 3: Multiply the divisor (x + 1) by the first term of the quotient (x) and subtract the result from the dividend. This gives you a new dividend of "-6x + 7".

Step 4: Repeat the process. Divide the first term of the new dividend (-6x) by the first term of the divisor (x) to get the second term of the quotient (-6).

Step 5: Multiply the divisor (x + 1) by the second term of the quotient (-6) and subtract the result from the new dividend. This gives you a remainder of "1".

So, when "x^2 - 5x + 7" is divided by "x + 1", the quotient is "x - 6" and the remainder is "1". This can be written as "x - 6 + 1/(x + 1)".