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Mathematics
Mathematics
Problem
Consider the polynomial
f
(
x
)
=
x
4
+
a
x
3
−
6
x
+
2
f(x)=x^{4}+ax^{3}-6x+2
f
(
x
)
=
x
4
+
a
x
3
−
6
x
+
2
. (i) Given that
f
(
1
)
=
8
f(1)=8
f
(
1
)
=
8
, determine the value of
a
a
a
. (ii) Using the value of
a
a
a
obtained in part (i), calculate the remainder when
f
(
x
)
f(x)
f
(
x
)
is divided by
(
x
+
2
)
(x+2)
(
x
+
2
)
.
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