To simplify and rewrite the mathematical expression [tex]\(-x + 4x^2 - 12\)[/tex], let's follow these steps:
1. Identify each term in the expression:
- The first term is [tex]\(-x\)[/tex].
- The second term is [tex]\(4x^2\)[/tex].
- The third term is [tex]\(-12\)[/tex].
2. Rewrite the expression in a more conventional order (usually descending powers of [tex]\(x\)[/tex]):
Expressions are typically ordered starting with the term having the highest power of [tex]\(x\)[/tex], which helps with readability and further manipulation.
- The term with the highest power of [tex]\(x\)[/tex] is [tex]\(4x^2\)[/tex].
- The next term is [tex]\(-x\)[/tex], which has a power of 1.
- The constant term is [tex]\(-12\)[/tex].
3. Combine these terms in the appropriate order:
[tex]\[
4x^2 - x - 12
\][/tex]
Thus, the given expression [tex]\(-x + 4x^2 - 12\)[/tex] can be rewritten and simplified as:
[tex]\[
4x^2 - x - 12
\][/tex]
This is your simplified polynomial in standard form.
