Subtract $x^{5} - 2 x^{2} - 3 x$ form $x^{3} + 3 x^{2} + 1$

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Solution

$(x^{3} + 3 x^{2} + 1) - (x^{5} - 2 x^{2} - 3 x)$
open the brackets and change the sign
$x^{3} + 3 x^{2} + 1 - x^{5} + 2 x^{2} + 3 x$
Rearrange into standard form and combine like terms
$- x^{5} + x^{3} + 5 x^{2} + 3 x + 1$

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