Step 1: First we have to write polynomials in descending order.

$$ \begin{aligned} P(x) &= -x^3+4x^2-5 \\ Q(x) &= -6x^3-3x^2+3 \\ \end{aligned} $$

Step 2: Write second polynomial below the first one. Making sure like terms are lined up.

$$ \begin{array}{lrrr} & -x^3 & 4x^2 & -5 \\ \color{red}{ - } & -6x^3 & -3x^2 & 3 \\ \hline \end{array} $$

Step 3: Change ALL the signs in the second row.

$$ \begin{array}{lrrr} & -x^3 & 4x^2 & -5 \\ \color{red}{ - } & 6x^3 & 3x^2 & -3 \\ \hline \end{array} $$

Step 4: Combine like terms (add each column):

$$ \begin{array}{lrrr} & -x^3 & 4x^2 & -5 \\ \color{red}{ - } & 6x^3 & 3x^2 & -3 \\ \hline & -7x^3 & x^2 & -2 \end{array} $$

Polynomial Operations Calculator