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### Theory:

To subtract polynomials, first reverse the sign of each term we are subtracting (in other words turn "$$+$$" into "$$-$$", and "$$-$$" into "$$+$$"), then add as usual.
Example:
Subtract $p\left(x\right)=\mathit{5}+x-\mathit{2}{x}^{2}$ and  $q\left(x\right)=3x²\phantom{\rule{0.147em}{0ex}}-\phantom{\rule{0.147em}{0ex}}6x\phantom{\rule{0.147em}{0ex}}-\phantom{\rule{0.147em}{0ex}}4$.

$=\phantom{\rule{0.147em}{0ex}}-\phantom{\rule{0.147em}{0ex}}2x² +\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}x\phantom{\rule{0.147em}{0ex}}+\phantom{\rule{0.147em}{0ex}}5-\left(3x²\phantom{\rule{0.147em}{0ex}}-\phantom{\rule{0.147em}{0ex}}6x\phantom{\rule{0.147em}{0ex}}-\phantom{\rule{0.147em}{0ex}}4\right)$

Now change the sign of $$q(x)$$.

$$= -2x^2 + x +5-3x^2 +6x +4$$

$=-\phantom{\rule{0.147em}{0ex}}2x²-3x²\phantom{\rule{0.147em}{0ex}}+x+6x+5\phantom{\rule{0.147em}{0ex}}+4$

$=\left(-\phantom{\rule{0.147em}{0ex}}2-3\right)x²\phantom{\rule{0.147em}{0ex}}+\left(1+6\right)x+5\phantom{\rule{0.147em}{0ex}}+4$

$=-5x² +\phantom{\rule{0.147em}{0ex}}7x\phantom{\rule{0.147em}{0ex}}+\phantom{\rule{0.147em}{0ex}}9$