Factorise : x3 – 27 – x + 3
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Answer:
Let f(x) = x³ + 27
0 = x³ + 27
x³= -27
x = -3
This means that x = -3 is the only zero of the graph of f(x). Since we know
(
x
+
3
)
is one factor of
f
(
x
)
, to find the 2nd factor,
x
3
+
27
x
+
3
We get the second factor to be
x
2
−
3
x
+
9
.
Therefore,
f
(
x
)
=
(
x
+
3
)
(
x
2
−
3
x
+
9
)
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