Add $ \, \color{blue}{ 6x^2-11x+4 } \, $ and $ \, \color{orangered}{ x^2+10x-3x^3 }$.

$$ \left( \color{blue}{6x^2-11x+4} \right) + \left( \color{orangered}{x^2+10x-3x^3} \right) = -3x^3+7x^2-x+4 $$

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

$$ \begin{aligned} P(x) &= 6x^2-11x+4 \\ Q(x) &= -3x^3+x^2+10x \\ \end{aligned} $$

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

$$ \begin{array}{lrrrr} & & 6x^2 & -11x & 4 \\ \color{blue}{ + } & -3x^3 & x^2 & 10x & \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & & 6x^2 & -11x & 4 \\ \color{blue}{ + } & -3x^3 & x^2 & 10x & \\ \hline & -3x^3 & 7x^2 & -x & 4 \end{array} $$

Polynomial Operations Calculator