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Omni-MATH / We define two types of operation on polynomial of third degree:

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problem

We define two types of operation on polynomial of third degree: a) switch places of the coefficients of polynomial(including zero coefficients), ex: x3+x2+3x−2 x^3+x^2+3x-2 => −2x3+3x2+x+1 -2x^3+3x^2+x+1 b) replace the polynomial P(x)P(x) with P(x+1)P(x+1) If limitless amount of operations is allowed, is it possible from x3−2x^3-2 to get x3−3x2+3x−3x^3-3x^2+3x-3 ?
Plain-text mathematical notation (without MathML)
We define two types of operation on polynomial of third degree:
a) switch places of the coefficients of polynomial(including zero coefficients), ex:
x³+x²+3x−2 => −2x³+3x²+x+1
b) replace the polynomial P(x) with P(x+1)
If limitless amount of operations is allowed,
is it possible from x³−2 to get x³−3x²+3x−3 ?
Original LaTeX notation
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+3x-2 $ => $ -2x^3+3x^2+x+1$
b) replace the polynomial $P(x)$ with $P(x+1)$
If limitless amount of operations is allowed,
is it possible from $x^3-2$ to get $x^3-3x^2+3x-3$ ?

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Source and history

task_id
74366f36-5e1b-53b7-948d-6bedeed2fd73
task_key
test--74366f36-5e1b-53b7-948d-6bedeed2fd73
task_revision_id
1
config / split
/ test

Official source

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