🔒 sympy

[hoary zodiac]

from sympy import symbols, gcd

x = symbols('x')

p1 = x**4 + 2*x**3 + 3*x**2 + 2*x + 1
p2 = x**4 - 2*x**2 - 3*x - 2


print(gcd(p2, p1))

when i do this in python i get x**2 + x + 1 as the result but if i do this using Euclidian's algorithm by hand i get that the answer is 1 and when i do this using a calculator (symbolab) i get that the answer is also 1 so what am i missing here?

[warped yarrow]

@hoary zodiac

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[hoary zodiac]

!eval ```py
from sympy import symbols, gcd

x = symbols('x')

p1 = x4 + 2*x3 + 3x**2 + 2x + 1
p2 = x4 - 2*x2 - 3*x - 2

print(gcd(p2, p1))

[warped yarrow]

:white_check_mark: Your 3.12 eval job has completed with return code 0.

x**2 + x + 1

[tight summit]

Get sympy to factorise both quartics.

from sympy import symbols, factor

# Define the variable
x = symbols('x')

# Define the quartic polynomial
p1 = x**4 + 2*x**3 + 3*x**2 + 2*x + 1
p2 = x**4 - 2*x**2 - 3*x - 2

print(factor(p1))
print(factor(p2))

(x**2 + x + 1)**2
(x - 2)*(x + 1)*(x**2 + x + 1)

I think there was a mistake in the hand calculation.

[civic sinew]

and symbolab fails to factor for some reason

wolfram alpha does it fine

[tight summit]

Is symbolab thrown off by complex roots?

[warped yarrow]

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