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Problem
Problem
f
(
x
)
=
3
x
3
+
4
x
2
+
13
x
+
4
f(x) = 3x^3 + 4x^2 + 13x + 4
f
(
x
)
=
3
x
3
+
4
x
2
+
13
x
+
4
a. Show that
(
3
x
+
1
)
(3x + 1)
(
3
x
+
1
)
is a factor of
f
(
x
)
f(x)
f
(
x
)
. b. Factorise
f
(
x
)
f(x)
f
(
x
)
completely. c. Prove that there are no real solutions to
3
sec
2
θ
+
4
sec
θ
+
13
+
4
cos
θ
=
0
3 \sec^2 \theta + 4 \sec \theta + 13 + 4 \cos \theta = 0
3
sec
2
θ
+
4
sec
θ
+
13
+
4
cos
θ
=
0
.
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