How can I sort the polynomial by the degree of $x$

Question

f1 = a x^2 + b x + c + x^3

(* a x^2+b x+c+x^3 *)

f1 /. x -> (x - a/3) // Expand

(* (2 a^3)/27-(a^2 x)/3-(a b)/3+b x+c+x^3 *)

I've tried this:

f1 /. x -> (x - a/3) // Expand // Collect[#, x] &

(* (2 a^3)/27+x (b-a^2/3)-(a b)/3+c+x^3 *)

f1 /. x -> (x - a/3) // Expand // Collect[#, x] & // PolynomialForm

(* (2 a^3)/27-(b a)/3+x^3+c+(b-a^2/3) x *)

You can extract the coefficients of $x$ as a list using f1 /. x -> (x - a/3) // CoefficientList[#, x] &. — Stephen Luttrell
– Stephen Luttrell, Commented Nov 19, 2013 at 17:36

Community · Accepted Answer · 2017-04-13 12:55:59Z

Try this formatting

OrderedForm[x_] := HoldForm[+##] & @@ (x^#1[[1]] #2 & @@@ CoefficientRules[#, x]) &; f1 /. x -> (x - a/3) // OrderedForm[x]

x^3+(-(a^2/3)+b) x+((2 a^3)/27-(a b)/3+c)

See also my answer here.

J. M.'s missing motivation · Accepted Answer · 2020-05-14 01:21:51Z

The OP almost had it with attempting to use PolynomialForm[]. All that was missing is the use of an appropriate setting:

PolynomialForm[a x^2 + b x + c + x^3 /. x -> (x - a/3), TraditionalOrder -> True] (x - a/3)^3 + a (x - a/3)^2 + b (x - a/3) + c

As is usual with *Form[] functions, this is only suitable for display/pretty printing.

2 Answers 2