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Byju's Answer
Standard IX
Mathematics
Factor Theorem
Find the rema...
Question
Find the remainder when :
p
(
x
)
=
3
x
3
−
4
x
2
+
7
x
+
5
is divided by
(
x
−
3
)
and
(
x
+
3
)
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Solution
p
(
x
)
=
3
x
3
−
4
x
2
+
7
x
+
5
According to remainder theorm,
p
(
3
)
a
n
d
p
(
−
3
)
will give us the remainder
p
(
3
)
=
3
(
3
)
3
−
4
(
3
)
2
+
7
(
3
)
+
5
=
81
−
36
+
21
+
5
=
71
p
(
−
3
)
=
3
(
−
3
)
3
−
4
(
−
3
)
2
+
7
(
−
3
)
+
5
=
−
81
−
36
−
21
+
5
=
−
133
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1
Similar questions
Q.
Find the remainder when
p
(
x
)
=
−
3
x
3
−
4
x
2
+
10
x
−
7
is divided by
x
−
2
Q.
A polynomial p(x) is divided by (2x - 1). The quotient and remainder obtained are
(
7
x
2
+
x
+
5
)
and 4 respectively. Find p(x).
OR
Find the quotient and remainder using synthetic division.
(
3
x
3
−
2
x
2
+
7
x
−
5
)
÷
(
x
+
3
)
.
Q.
The polynomial
p
(
x
)
=
a
x
3
+
4
x
2
+
3
x
−
4
and
q
(
x
)
=
x
3
−
4
x
+
a
leave same remainder when divided by
(
x
−
3
)
. Find
a
and hence find the remainder when
p
(
x
)
is divided by
(
x
−
2
)
.
Q.
If
p
(
x
)
=
2
x
4
−
3
x
3
−
5
x
2
+
8
x
−
3
, find the remainder when
p
(
x
)
is divided by
(
x
−
3
2
)
. Also, verify the result by actual division.
Q.
When
3
x
3
−
7
x
+
7
is divided by
x
+
2
, find the remainder.
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