Question
Express the polynomial \( -6 + 2x^4 + x \) in standard form.
Ask by Savage Graham. in Italy
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The polynomial in standard form is \( 2x^4 + x - 6 \).
Solution
To express the polynomial \( -6 + 2x^4 + x \) in standard form, arrange the terms in descending order of their degrees (from highest to lowest).
1. Identify the degrees of each term:
- \( 2x^4 \) has a degree of 4.
- \( x \) has a degree of 1.
- \( -6 \) is a constant term with a degree of 0.
2. Arrange the terms from highest to lowest degree:
\[
2x^4 + x - 6
\]
**Standard Form:**
\[
2x^4 + x - 6
\]
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Simplify this solution Bonus Knowledge
To express the polynomial \( -6 + 2x^4 + x \) in standard form, we rearrange the terms in descending order based on the exponents of \( x \). The term with the highest degree is \( 2x^4 \), followed by \( x \) (which is \( 1x^1 \)), and finally the constant term \( -6 \). Thus, the polynomial in standard form is: \[ 2x^4 + x - 6 \]
