Certainly! Let's delve into the given quadratic expression step-by-step:
[tex]\[ a x^2 - (a^2 + 1) x + a \][/tex]
Here, it seems like the notation "[tex]\(\mid\)[/tex]" might be indicating that we are supposed to work with the given quadratic expression [tex]\(a x^2 - (a^2 + 1) x + a\)[/tex].
To understand this expression better, it will be helpful to rewrite it in a standard form, which is typically expressed as [tex]\( ax^2 + bx + c \)[/tex].
Given the quadratic expression:
[tex]\[ a x^2 - (a^2 + 1) x + a \][/tex]
We can identify the coefficients for each term:
- The coefficient of [tex]\(x^2\)[/tex] is [tex]\(a\)[/tex].
- The coefficient of [tex]\(x\)[/tex] is [tex]\(- (a^2 + 1)\)[/tex].
- The constant term is [tex]\(a\)[/tex].
Combining these terms, we can express it in a simplified form:
[tex]\[ a x^2 + a - x (a^2 + 1) \][/tex]
The expression broken down:
1. [tex]\(a x^2\)[/tex]
2. [tex]\(- (a^2 + 1) x\)[/tex]
3. [tex]\(a\)[/tex]
Thus, the entire quadratic equation can be articulated as:
[tex]\[ a x^2 + a - x (a^2 + 1) \][/tex]
So, the detailed form of the quadratic expression is:
[tex]\[ \boxed{a x^2 + a - x (a^2 + 1)} \][/tex]
This equation represents a quadratic relationship in terms of [tex]\(x\)[/tex] with given coefficients that depend on the parameter [tex]\(a\)[/tex].
