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The problem is that the x in polynomial is not the x = var('x'):

>>> x is polynomial.variables()[0]
False

It is better to be explicit:

>>> x = SR.var('x')
>>> polynomial = x**2 - 2
>>> polynomial.find(x**w0+w1)
[x^2 - 2]
>>> polynomial.match(x**w0+w1)
{$1: -2, $0: 2}

The problem is that the x in polynomial is not the x = var('x'):

>>> x is polynomial.variables()[0]
False

It is better to be explicit:

>>> x = SR.var('x')
>>> polynomial = x**2 - 2
>>> polynomial.find(x**w0+w1)
[x^2 - 2]
>>> polynomial.match(x**w0+w1)
{$1: -2, $0: 2}

>>> x = SR.var('x')
>>> polynomial = sage_eval('x^2 - 2', locals={'x' : x})