Question

Nothing.

Answer 1

I don't know why these statements are listed in this particular order...
it's sort of weird.

You would normally list the possible roots BEFORE you actually find them.

But anyway, if you apply synthetic division with one of the roots,
you will always end up with a remainder of zero,
and you'll never get zero remainder with a non-root.

Notice that in statement 3, they used a value which is not a root, x=5,
and they got a remainder of zero! :O Oh noes!

Answer 2

You could maybe say something like...

x=5 is not a root of this polynomial,
therefore it should produce a remainder.

I dunno, that's my thinking at least :D

Answer 3

Or another way to justify your answer is by looking very carefully at the synthetic division that they applied. One of the columns of addition was done incorrectly. (Pssst -25 + 45 does not equal 7).