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Prove by contradiction that there exists no function f(x) = 2x^3 + bx^2 + cx + 3
MATHEMATICS · Subjective · A Level · Mathematics · Proof · Proof
Problem
Prove by contradiction that there exists no function
f
(
x
)
=
2
x
3
+
b
x
2
+
c
x
+
3
,
where
b
,
c
∈
Z
f(x) = 2x^3 + bx^2 + cx + 3,\ \text{where } b, c \in \mathbb{Z}
f
(
x
)
=
2
x
3
+
b
x
2
+
c
x
+
3
,
where
b
,
c
∈
Z
such that
(
2
x
+
3
)
(2x + 3)
(
2
x
+
3
)
is a factor of
f
(
x
)
f(x)
f
(
x
)
, and when
f
(
x
)
f(x)
f
(
x
)
is divided by
x
−
2
x - 2
x
−
2
the remainder is 5.
Related theory
Polynomials
Mathematical Logic
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