How can we tell by looking at the remainder that an error was made somewhere for the picture below?

Question

 

How can we tell by looking at the remainder that an error was made somewhere?

Answer 1

The remainder in the image is 990. When the remainder is other than zero, then x + 9 is not one of the factors of the original polynomial.

Unfortunately, there is a typo in the earlier step. When you do x³ + 9x², you need to set both to negative since you are subtracting it from x³ + 7x² to get -2x² and bring down -26x. Then you repeat the steps until the end and the remainder should be zero.

For that, x + 9 should be one of the factors of the original polynomial.