Question
Rewrite the following polynomial in standard form.
x, cubed, plus, one half, x, to the power 4 , plus, 8
x
3
+
2
1
x
4
+8
x, cubed, plus, one half, x, to the power 4 , plus, 8
x
3
+
2
1
x
4
+8
Answers
GPT-4o mini
To rewrite the polynomial \( x^3 + \frac{1}{2} x^4 + 8 \) in standard form, we order the terms by decreasing degree of \( x \). The standard form places the highest power of \( x \) first:
1. Identify the terms: \( \frac{1}{2} x^4 \), \( x^3 \), and \( 8 \).
2. Start with the highest degree: \( \frac{1}{2} x^4 \).
3. Next is \( x^3 \).
4. Lastly, the constant term is \( 8 \).
Putting it all together, the polynomial in standard form is:
\[
\frac{1}{2} x^4 + x^3 + 8
\]
1. Identify the terms: \( \frac{1}{2} x^4 \), \( x^3 \), and \( 8 \).
2. Start with the highest degree: \( \frac{1}{2} x^4 \).
3. Next is \( x^3 \).
4. Lastly, the constant term is \( 8 \).
Putting it all together, the polynomial in standard form is:
\[
\frac{1}{2} x^4 + x^3 + 8
\]