divide x*3 - 2 X*2 + X + 1 by X - 2
Answers
Answer:
Step-by-step explanation:
The Quotient Poly.
=
x
2
−
x
−
4
.
The Remainder=
−
2
.
Explanation:
We can perform the Long Division and get the Quotient and the
Remainder. But, here is another way to solve the Problem.
Suppose that, when
P
(
x
)
=
x
3
−
2
x
2
−
3
x
+
2
is divided by
(
x
−
1
)
, the Quotient Poly. is
Q
(
x
)
and the remainder
R
.
Note
that, since the divisor
9
x
−
1
)
is a Linear Poly., the Remainder has
to be a constant.
The well-known relation btwn.
P
(
x
)
,
Q
(
x
)
,
(
x
−
1
)
and
,
R
is
given by,
P
(
x
)
=
(
x
−
1
)
Q
(
x
)
+
R
,
i.e.,
x
3
−
2
x
2
−
3
x
+
2
=
(
x
−
1
)
Q
(
x
)
+
R
...
...
...
...
...
...
...
...
(
⋆
)
Sub.ing,
x
=
1
in
(
⋆
)
,
1
−
2
−
3
+
2
=
(
1
−
1
)
Q
(
x
)
+
R
∴
R
=
−
2
.
Then, sub.ing
R
=
−
2
in
(
⋆
)
,
x
3
−
2
x
2
−
3
x
+
2
=
(
x
−
1
)
Q
(
x
)
−
2
,
or
,
x
3
−
2
x
2
−
3
x
+
4
=
(
x
−
1
)
Q
(
x
)
⇒
Q
(
x
)
=
x
3
−
2
x
2
−
3
x
+
4
x
−
1
=
x
3
−
x
2
−
x
2
+
x
−
4
x
+
4
x
−
1
=
x
2
(
x
−
1
)
−
x
(
x
−
1
)
−
4
(
x
−
1
)
x
−
1
=
(
x
−
1
)
(
x
2
−
x
−
4
)
(
x
−
1
)
∴
Q
(
x
)
=
x
2
−
x
−
4
.