To write the given polynomial [tex]\( 16x^2 - \frac{x^4}{6} \)[/tex] in standard form, let's follow these steps:
1. Identify the polynomial: The given polynomial is [tex]\( 16x^2 - \frac{x^4}{6} \)[/tex].
2. Simplify the terms: Since this polynomial already has its terms separated, we need to simplify it as much as possible.
3. Rewrite in standard form: The standard form for a polynomial is writing it in descending order of powers, so we will arrange the terms from the highest power of [tex]\(x\)[/tex] to the lowest.
4. Combine like terms (if any) and factor common terms, if useful for simplifications: Here, we can multiply and combine terms under a common factor:
[tex]\( 16x^2 - \frac{x^4}{6} \)[/tex]
= [tex]\( \frac{96x^2}{6} - \frac{x^4}{6} \)[/tex]
= [tex]\( \frac{96x^2 - x^4}{6} \)[/tex]
5. Recognize a pattern if visible: We notice that within the parenthesis, we have [tex]\( x^2 \)[/tex] common in both terms:
= [tex]\( \frac{x^2 (96 - x^2)}{6} \)[/tex]
6. Final expression: The polynomial [tex]\( 16x^2 - \frac{x^4}{6} \)[/tex] written in its simplified standard form is:
[tex]\( \frac{x^2 (96 - x^2)}{6} \)[/tex]
So, the simplified standard form of the polynomial [tex]\( 16x^2 - \frac{x^4}{6} \)[/tex] is:
[tex]\[ \frac{x^2 (96 - x^2)}{6} \][/tex]
