Add $ \, \color{blue}{ -12x^4+10x^5+2x^3 } \, $ and $ \, \color{orangered}{ 14x^3+115x+8x^4 }$.

$$ \left( \color{blue}{-12x^4+10x^5+2x^3} \right) + \left( \color{orangered}{14x^3+115x+8x^4} \right) = 10x^5-4x^4+16x^3+115x $$

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

$$ \begin{aligned} P(x) &= 10x^5-12x^4+2x^3 \\ Q(x) &= 8x^4+14x^3+115x \\ \end{aligned} $$

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

$$ \begin{array}{lrrrr} & 10x^5 & -12x^4 & 2x^3 & \\ \color{blue}{ + } & & 8x^4 & 14x^3 & 115x \\ \hline \end{array} $$

Step 3: Combine like terms (add each column):

$$ \begin{array}{lrrrr} & 10x^5 & -12x^4 & 2x^3 & \\ \color{blue}{ + } & & 8x^4 & 14x^3 & 115x \\ \hline & 10x^5 & -4x^4 & 16x^3 & 115x \end{array} $$

Polynomial Operations Calculator