Let’s expand the given function [tex]\( f(x) \)[/tex].
Given:
[tex]\[ f(x) = x^3 - a x^2 + b x - c \][/tex]
It looks like our goal is to describe the function in its expanded form. Breaking down each part of the given function, we have three terms involving variables [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex]:
1. The first term is [tex]\(x^3\)[/tex], which remains as it is.
2. The second term involves [tex]\(a\)[/tex] and is [tex]\(- a x^2\)[/tex].
3. The third term involves [tex]\(b\)[/tex] and is [tex]\(+ b x\)[/tex].
4. Finally, there is a constant term involving [tex]\(c\)[/tex], which is [tex]\(- c\)[/tex].
Putting these terms together, the function [tex]\(f(x)\)[/tex] in its expanded form is:
[tex]\[ f(x) = x^3 - a x^2 + b x - c \][/tex]
Therefore, the expanded form of the function is:
[tex]\[ f(x) = -a x^2 + b x - c + x^3 \][/tex]
And the placeholders involved here are:
[tex]\[ a, b, c \][/tex]
Hence, we see that the function [tex]\(f(x)\)[/tex] when fully written out is:
[tex]\[ f(x) = x^3 - a x^2 + b x - c \][/tex]
And represented along with its placeholders, it becomes:
[tex]\[ ( x^3 - a x^2 + b x - c, (a, b, c) ) \][/tex]
