Hi Paige! Here are my workings for this question.

In your working,

(x - 7) times (x2 - 14x + 49) - 4x + 28 cannot be simplified to (x - 7) (x2 - 18x + 77)

since the "times" connecting the (x - 7) and the (x2 - 14x + 49) takes precedence in the rule of operations over the outside "-4x + 28".

Instead, it only simplifies to such had the starting the expression been

(x - 7) [(x2 - 14x + 49) - 4x + 28].

For the second part, we look for the signages of (x - 5), (x - 7) and (x - 9) for different values of x.

The expression can only be positive when exactly two of the three expressions are negative or exactly none of the three expressions are negative.

This means that x must lie between 5 or 7 or x must lie fully above 9.

The smallest integer value of x must be 6 (while the next integer value is 10).

Let me know if you need further explanation and I will do my best to explain them again.