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

$$ \begin{aligned} P(x) &= 12x^2-8x+11 \\ Q(x) &= 10x^2-6x-14 \\ \end{aligned} $$

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

$$ \begin{array}{lrrr} & 12x^2 & -8x & 11 \\ \color{red}{ - } & 10x^2 & -6x & -14 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & 12x^2 & -8x & 11 \\ \color{red}{ - } & -10x^2 & 6x & 14 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & 12x^2 & -8x & 11 \\ \color{red}{ - } & -10x^2 & 6x & 14 \\ \hline & 22x^2 & -14x & -3 \end{array} $$

Polynomial Operations Calculator