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Belgium Contests
Flanders Math Olympiad
2014 Flanders Math Olympiad
4
4
Part of
2014 Flanders Math Olympiad
Problems
(1)
a + b=? remainder P(x):(x^3 + ax + b)=remainder P(x):(x^3 + ax^2 + b)
Source: Flanders Math Olympiad 2014 p4
12/24/2022
Let
P
(
x
)
P(x)
P
(
x
)
be a polynomial of degree
5
5
5
and suppose that a and b are real numbers different from zero. Suppose the remainder when
P
(
x
)
P(x)
P
(
x
)
is divided by
x
3
+
a
x
+
b
x^3 + ax + b
x
3
+
a
x
+
b
equals the remainder when
P
(
x
)
P(x)
P
(
x
)
is divided by
x
3
+
a
x
2
+
b
x^3 + ax^2 + b
x
3
+
a
x
2
+
b
. Then determine
a
+
b
a + b
a
+
b
.
algebra
polynomial