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Byju's Answer
Standard IX
Mathematics
Factor Theorem
Check the val...
Question
Check the validity of the statement:
(
x
+
2
)
is a factor of
p
(
x
)
=
x
3
+
x
2
+
x
+
2
.
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Solution
To check:
(
x
+
2
)
is a factor of
p
(
x
)
=
x
3
+
x
2
+
x
+
2
Putting,
x
+
2
=
0
⇒
x
=
−
2
Putting value of
x
=
−
2
in
p
(
x
)
p
(
−
2
)
=
(
−
2
)
3
+
(
−
2
)
2
+
(
−
2
)
+
2
=
−
8
+
4
−
2
+
2
=
−
4
It is not equal to
0
Hence,
x
+
2
is not a factor of
p
(
x
)
.
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0
Similar questions
Q.
Check whether
x
2
−
x
+
1
is a factor in
x
3
−
3
x
2
+
3
x
−
2
Q.
Check
x
2
−
x
+
1
is a factor of
x
3
−
3
x
2
−
3
x
−
2
Q.
Check whether,
x
−
2
is a factor of the polynomial
x
3
−
x
2
−
4
by using factor theorem.
Q.
Question 2
Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases:
(
i
)
p
(
x
)
=
2
x
3
+
x
2
−
2
x
−
1
,
g
(
x
)
=
x
+
1
(
i
i
)
p
(
x
)
=
x
3
+
3
x
2
+
3
x
+
1
,
g
(
x
)
=
x
+
2
(
i
i
i
)
p
(
x
)
=
x
3
−
4
x
2
+
x
+
6
,
g
(
x
)
=
x
−
3
Q.
Use the Factor Theorem to determine whether
g
(
x
)
is a factor of
p
(
x
)
in each of the following cases:
(i)
p
(
x
)
=
2
x
3
+
x
2
−
2
x
−
1
,
g
(
x
)
=
x
+
1
(ii)
p
(
x
)
=
x
3
+
3
x
2
+
3
x
+
1
,
g
(
x
)
=
x
+
2
(iii)
p
(
x
)
=
x
3
−
4
x
2
+
x
+
6
,
g
(
x
)
=
x
−
3
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