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Mathematics
Problem
For the polynomial
t
(
x
)
=
2
x
3
−
5
x
2
−
4
x
+
12
t(x)=2x^{3}-5x^{2}-4x+12
t
(
x
)
=
2
x
3
−
5
x
2
−
4
x
+
12
, it is known that
x
−
2
x-2
x
−
2
is one of its factors. Which of the following gives the complete factorisation of
t
(
x
)
t(x)
t
(
x
)
? a)
(
x
−
2
)
2
(
2
x
+
3
)
(x-2)^2(2x+3)
(
x
−
2
)
2
(
2
x
+
3
)
b)
(
x
−
2
)
2
(
2
x
−
3
)
(x-2)^2(2x-3)
(
x
−
2
)
2
(
2
x
−
3
)
c)
(
x
−
2
)
(
2
x
+
3
)
(
x
+
2
)
(x-2)(2x+3)(x+2)
(
x
−
2
)
(
2
x
+
3
)
(
x
+
2
)
d)
(
x
−
2
)
(
x
+
3
)
(
2
x
+
3
)
(x-2)(x+3)(2x+3)
(
x
−
2
)
(
x
+
3
)
(
2
x
+
3
)
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