Let’s suppose that we have polynomial
of degree greater than equal to 1 and
is a polynomial of degree equal to 1.
Remainder theorem states that when
is divided by
then remainder is equal to
. Let’s cover some examples.
Find the remainder when
is divided by
.
Here, we have
and
.
Therefore, remainder =
Is
divisible by
?
or
Is 2 zero of the polynomial
?
We can again use remainder theorem to check this. Here, we have
and
.
Therefore, remainder =
.
Remainder equal to 0 means that
is divisible by
. It also means that 2 is the zero of polynomial
.
Is
divisible by
.
Or
Is -2 zero of the polynomial
?
In this problem, we have
and
.
because
. Read remainder theorem carefully.
Therefore, remainder
Remainder is equal to 0 which means that
is divisible by
. It also means that -2 is the zero of polynomial
.
GMAT Sample Problem:
What is the remainder when
is divided by
?
(A) 1
(B) 77
(C) 2
(D) -1
(E) None of these
Again using the remainder theorem, we can find the remainder when
is divided by
.
Here, we have
. Therefore, remainder =
.
Therefore, the answer is (D).
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