When a polynomial is divided by (x+2), the remainder is -19. When the same polynomial is divided by (x-1), the remainder is 2, how do you determine the remainder when the polynomial is divided by (x+2)(x-1)?
3 Answers
The remainder when dividing
Explanation:
Note that
Suppose
Then:
Hence [1]:
Hence [2]:
Subtract [2] from [1] to get
Then
So the remainder when dividing
The remainder is
Explanation:
Call the polynomial
Because
Because
From these two facts we get:
So
and
Applying the Division Algorithm and the Remainder Theorem to
Subtitutuing in
# = (x+2)(x-1)Q_2(x) + 7(x+2) - 19#
# = (x+2)(x-1)Q_2(x) + 7x+ 14 - 19#
# = (x+2)(x-1)Q_2(x) + [7x - 5]#
The remainder is
Explanation:
Let the Poly. in question be
We know that, the Degree of the Remainder Poly. is strictly
less than that of the Divisor Poly.
So, when
Remainder Ploly. must have a degree
Therefore, let us suppose that, the desired remainder is,
Symbolically, this can be said, as, let,
Now,
On the same lines,
Solving
remainder,
readily obtained.
Enjoy Maths.!