Write the polynomial in standard form
Identify the degree and leading coefficient
Determine the end behavior from the leading term
Find the x-intercepts by solving the polynomial equal to zero
Determine the multiplicity of each x-intercept
Find the y-intercept by evaluating the polynomial at x = 0
Use the degree and multiplicities to sketch the general shape
Plot the intercepts on the coordinate plane
Add additional points if needed for accuracy
Draw a smooth curve through the points
Check that the graph matches the end behavior and intercept behavior