ANSWER TO QUESTION 1
Given
We can use the factor theorem to determine if
is a factor of the polynomial or not.
According to this theorem, if is a factor of , then .
How did we get the ?
We set and then solve to obtain .
So now let us plug in in to the function to see if it will simplify to zero.
Since the result simplifies to zero, we conclude that
is a factor of
ANSWER TO QUESTION 2
We have the function,
We can use the remainder theorem to show that
is NOT a factor of the polynomial.
According to this theorem, if is not a factor of , then .
So now let us plug in in to the function to see if it will simplify to non-zero number.
Since the result simplifies to a non zero number, we conclude that
is NOT a factor of