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Mathematics
Mathematics
Problem
Let
t
t
t
be any real number and let
p
(
x
)
=
4
x
3
−
3
x
2
+
2
x
−
5
p(x)=4x^{3}-3x^{2}+2x-5
p
(
x
)
=
4
x
3
−
3
x
2
+
2
x
−
5
. a. (i) Find the remainder obtained when
p
(
x
)
p(x)
p
(
x
)
is divided by
x
−
(
2
t
+
1
)
x-(2t+1)
x
−
(
2
t
+
1
)
, expressing your answer in terms of
t
t
t
. b. (ii) Using your result from part (i), determine the remainder when
t
=
2
t=2
t
=
2
.
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