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Mathematics
Mathematics
Problem
The polynomial
p
(
x
)
=
x
4
−
5
x
3
+
a
x
2
+
b
x
+
12
p(x)=x^{4}-5x^{3}+ax^{2}+bx+12
p
(
x
)
=
x
4
−
5
x
3
+
a
x
2
+
b
x
+
12
is divisible by both
x
−
2
x-2
x
−
2
and
x
−
3
x-3
x
−
3
. (i) Find the values of
a
a
a
and
b
b
b
. (ii) Using the values of
a
a
a
and
b
b
b
found in part (i), factorise
p
(
x
)
p(x)
p
(
x
)
completely.
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