Question
Rewrite the following polynomial in standard form.
minus, start fraction, x, squared, divided by, 8, end fraction, plus, 1, plus, 5, x, cubed, minus, x, to the power 4
−
8
x
2
+1+5x
3
−x
4
minus, start fraction, x, squared, divided by, 8, end fraction, plus, 1, plus, 5, x, cubed, minus, x, to the power 4
−
8
x
2
+1+5x
3
−x
4
Answers
GPT-4o mini
To rewrite the polynomial in standard form, we need to arrange the terms in descending order of their degrees. Here’s the given polynomial:
\[
-\frac{x^2}{8} + 1 + 5x^3 - x^4
\]
Now, let's reorder the terms by moving the highest degree term first, followed by the others.
1. The term with the highest degree is \(-x^4\).
2. Next is \(5x^3\).
3. After that is \(-\frac{x^2}{8}\).
4. Finally, the constant term is \(1\).
Putting it all together in standard form, we have:
\[
-x^4 + 5x^3 - \frac{x^2}{8} + 1
\]
This is the polynomial written in standard form.
\[
-\frac{x^2}{8} + 1 + 5x^3 - x^4
\]
Now, let's reorder the terms by moving the highest degree term first, followed by the others.
1. The term with the highest degree is \(-x^4\).
2. Next is \(5x^3\).
3. After that is \(-\frac{x^2}{8}\).
4. Finally, the constant term is \(1\).
Putting it all together in standard form, we have:
\[
-x^4 + 5x^3 - \frac{x^2}{8} + 1
\]
This is the polynomial written in standard form.