Question

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Answer 1

if r is a zero of g(x), then g(r) = 0.

If r is a zero of g(x) , then long division of g(x) / ( x - r ) has a remainder of zero.

so here
g(2) = 0

but

g(x) / ( x - 2) will have the remainder of zero , not g(x) / ( x + 2)

Answer 2

now we need to find the names of these theorems that we are using

Answer 3

I have no clue which theorems we're using

Answer 4

So the first one is right?

Answer 5

I got it now, The second one is wrong because you have to use the opposite sign.