Write the polynomial in standard form
Identify the degree and leading coefficient
Determine the end behavior from the degree and leading coefficient
Find the y-intercept by evaluating the function at x = 0
Find the x-intercepts by setting the polynomial equal to 0
Factor the polynomial if possible
Use the multiplicity of each zero to determine how the graph behaves at each x-intercept
Find additional points by choosing x-values and evaluating the function
Plot the intercepts and additional points on a coordinate plane
Sketch the graph using the end behavior and the plotted points
Check for symmetry if applicable
Verify the graph matches the degree, intercepts, and multiplicities