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Mathematics
Mathematics
Problem
Let
p
(
x
)
=
4
x
4
−
7
x
3
+
2
x
2
−
5
x
+
11
p(x)=4x^{4}-7x^{3}+2x^{2}-5x+11
p
(
x
)
=
4
x
4
−
7
x
3
+
2
x
2
−
5
x
+
11
. (a) Find the remainder when
p
(
x
)
p(x)
p
(
x
)
is divided by
(
x
−
2
)
(x-2)
(
x
−
2
)
. (b) Find the remainder when
p
(
x
)
p(x)
p
(
x
)
is divided by
(
x
+
1
)
(x+1)
(
x
+
1
)
. (c) State, with reason, whether any of the linear factors
(
x
−
2
)
(x-2)
(
x
−
2
)
or
(
x
+
1
)
(x+1)
(
x
+
1
)
is a factor of
p
(
x
)
p(x)
p
(
x
)
.
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