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Byju's Answer
Standard IX
Mathematics
Factor Theorem
Find the rema...
Question
Find the remainder when
x
3
+
3
x
2
+
3
x
+
1
is divided by the following Linear polynomials:
5
+
2
x
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Solution
Given polynomial
x
3
+
3
x
2
+
3
x
+
1
divided by
5
+
2
x
If divided by
5
+
2
x
then
5
+
2
x
=
0
or
x
=
−
5
2
Replace x by
−
5
2
we get
p
(
x
)
=
x
3
+
3
x
2
+
3
x
+
1
p
(
−
5
2
)
=
(
−
5
2
)
3
+
3
(
−
5
2
)
2
+
3
(
−
5
2
)
+
1
⇒
p
(
−
5
2
)
=
−
125
8
+
75
4
−
15
2
+
1
⇒
(
−
5
2
)
=
−
125
+
150
−
60
+
8
8
=
−
27
8
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Similar questions
Q.
Find the remainder when
x
3
+
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2
+
3
x
+
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is divided by
5
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Q.
Find the remainder when the polynomial
x
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x
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is divided by
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Q.
The polynomial which when divided by −x
2
+ x − 1 gives a quotient x − 2 and remainder 3, is
(a) x
3
− 3x
2
+ 3x − 5
(b) −x
3
− 3x
2
− 3x − 5
(c) −x
3
+ 3x
2
− 3x + 5
(d) x
3
− 3x
2
− 3x + 5