o find the quotient and the remainder
when f(x) as devided by g (c)
f&c)=8823_60c2 + 158-7 gec)=2xti
Answers
Answered by
1
Answer:
Explanation:
Note that
(
x
+
2
)
(
x
−
1
)
=
x
2
+
x
−
2
is quadratic, so if we divide another polynomial by it then the remainder will be
0
, a non-zero constant or a linear polynomial. Any remainder of greater degree could be divided further.
Suppose
f
(
x
)
=
(
x
+
2
)
(
x
−
1
)
k
(
x
)
+
r
x
+
s
Then:
f
(
x
)
x
+
2
=
(
x
−
1
)
k
(
x
)
+
r
x
+
s
x
+
2
=
(
x
−
1
)
k
(
x
)
+
r
x
+
2
r
−
2
r
+
s
x
+
2
=
(
x
−
1
)
k
(
x
)
+
r
+
s
−
2
r
x
+
2
Hence [1]:
s
−
2
r
=
−
19
f
(
x
)
x
−
1
=
(
x
+
2
)
k
(
x
)
+
r
x
+
s
x
−
1
=
(
x
+
2
)
k
(
x
)
+
r
x
−
r
+
r
+
s
x
−
1
=
(
x
+
2
)
k
(
x
)
+
r
+
r
+
s
x
−
1
Hence [2]:
r
+
s
=
2
Subtract [2] from [1] to get
−
3
r
=
−
21
, hence
r
=
7
Then
s
=
2
−
r
=
−
5
So the remainder when dividing
f
(
x
)
by
(
x
+
2
)
(
x
−
1
)
is
7
x
−
5
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