Does this graph show a function? Explain how you know.
2 answers:
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Recall the polynomial remainder theorem: the remainder upon dividing a polynomial by
is equal to
. This means that
and
, which tell us
From here we can solve for :
so that
Now,
so the remainder upon dividing by
is
.
Next, if is a cubic function, then
is a linear polynomial that can be written as
. The coefficient of
in
is 1 (unity), so that expanding
gives us
and we also have that , so that
so that