Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2002 | Oct-Nov | (P2-9709/02) | Q#2
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Question
The polynomial is denoted by
. It is given that
is a factor of
, and that when
is divided by
the remainder is -5. Find the values of
and
.
Solution
We are given that;
We are also given that is a factor of
.
When a polynomial, , is divided by
, and
is factor of
, then the remainder is ZERO i.e.
.
We can write factor in standard form as;
Therefore;
We are also given that when is divided by
the remainder is -5.
When a polynomial, , is divided by a
, the remainder is the constant
We can write divisor in standard form as;
Therefore;
From we can substitute
in above equation;
Substitution of in any of these two equations yields value of
. We choose;
Hence;
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