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International Contests
International Zhautykov Olympiad
2019 International Zhautykov OIympiad
6
6
Part of
2019 International Zhautykov OIympiad
Problems
(1)
Polynomial (Izho)
Source: Izho
1/12/2019
We define two types of operation on polynomial of third degree: a) switch places of the coefficients of polynomial(including zero coefficients), ex:
x
3
+
x
2
+
3
x
−
2
x^3+x^2+3x-2
x
3
+
x
2
+
3
x
−
2
=>
−
2
x
3
+
3
x
2
+
x
+
1
-2x^3+3x^2+x+1
−
2
x
3
+
3
x
2
+
x
+
1
b) replace the polynomial
P
(
x
)
P(x)
P
(
x
)
with
P
(
x
+
1
)
P(x+1)
P
(
x
+
1
)
If limitless amount of operations is allowed, is it possible from
x
3
−
2
x^3-2
x
3
−
2
to get
x
3
−
3
x
2
+
3
x
−
3
x^3-3x^2+3x-3
x
3
−
3
x
2
+
3
x
−
3
?
polynomial
algebra
izho