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

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

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

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

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

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

Polynomial Operations Calculator