The standard form of a polynomial (which is what we have here) is written from highest exponent to lowest exponent. In addition, there should only be 1 of each exponent/variable pair (like x^4 or x^3). For example, here we have #3x^4# and #-x^4#; but we can only have 1 term with an #x^4# in it. To fix this, we need to combine these terms by adding #3x^4# to #-x^4#; the result is #2x^4# (remember that #3x^4+(-x^4)# is the same thing as #3x^4-x^4#).

From here, we just need to organize a bit - from highest exponent to lowest. Our highest is, of course, #4#. Then we have #3# - and since we don't have #x^2# or #x#, we ignore them. Now, what about the #-5#? Well, since #x^0 = 1#, we can write #-5# as #-5x^0#, which is the same thing as #-5*1# - which equals #-5#. That makes 0 our lowest exponent. Cool, huh?

Finally, we simply write it. We start with the term with the highest exponent (#2x^4#), and then go down from there. So, our polynomial in standard form is #2x^4+2x^3-5#. And we're done.