Question
Question Rewrite the following polynomial in standard form. \[ x^{3}+\frac{1}{2} x^{4}+8 \]
Ask by Campbell Montgomery. in the United States
Feb 26,2025
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Answer
The polynomial in standard form is \( \frac{1}{2}x^{4} + x^{3} + 8 \).
Solution
To rewrite the polynomial in standard form, arrange the terms in descending order by the exponent of x. Given:
x³ + ½x⁴ + 8
Rearrange so the highest exponent term comes first:
½x⁴ + x³ + 8
This is the polynomial in standard form.
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Simplify this solution Bonus Knowledge
To rewrite the polynomial in standard form, we want to arrange the terms in descending order of their degrees. The polynomial you've provided is: \[ x^{3}+\frac{1}{2} x^{4}+8 \] When we reorder it, we start with the term with the highest exponent, which is \(\frac{1}{2} x^{4}\), followed by \(x^{3}\), and then the constant term \(8\). Thus, the standard form of the polynomial is: \[ \frac{1}{2} x^{4} + x^{3} + 8 \]
