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Mathematics
Problem
2. Use the Factor Theorem to determine whether
g
(
x
)
g(x)
g
(
x
)
is a factor of
p
(
x
)
p(x)
p
(
x
)
in each of the following cases: (i)
p
(
x
)
=
2
x
3
+
x
2
−
2
x
−
1
,
g
(
x
)
=
x
+
1
p(x)=2 x^{3}+x^{2}-2 x-1, g(x)=x+1
p
(
x
)
=
2
x
3
+
x
2
−
2
x
−
1
,
g
(
x
)
=
x
+
1
(ii)
p
(
x
)
=
x
3
+
3
x
2
+
3
x
+
1
,
g
(
x
)
=
x
+
2
p(x)=x^{3}+3 x^{2}+3 x+1, g(x)=x+2
p
(
x
)
=
x
3
+
3
x
2
+
3
x
+
1
,
g
(
x
)
=
x
+
2
(iii)
p
(
x
)
=
x
3
−
4
x
2
+
x
+
6
,
g
(
x
)
=
x
−
3
p(x)=x^{3}-4 x^{2}+x+6, g(x)=x-3
p
(
x
)
=
x
3
−
4
x
2
+
x
+
6
,
g
(
x
)
=
x
−
3
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