Rewrite the following polynomial in standard form.

Question

5, plus, 2, x, to the power 5 , minus, start fraction, x, cubed, divided by, 7, end fraction, minus, 8, x, minus, 10, x, squared
5+2x
5
−
7
x
3

​
−8x−10x
2

Answer 1

To rewrite the polynomial in standard form, we need to arrange the terms in descending order of their degree. The polynomial you've provided is:

\[ 5 + 2x^5 - \frac{x^3}{7} - 8x - 10x^2 \]

First, we can express the polynomial more clearly:

1. The term \(2x^5\) is degree 5.
2. The term \(-\frac{x^3}{7}\) is degree 3.
3. The term \(-10x^2\) is degree 2.
4. The term \(-8x\) is degree 1.
5. The constant term is \(5\).

Now, we’ll organize the terms in descending order:

\[ 2x^5 - \frac{1}{7}x^3 - 10x^2 - 8x + 5 \]

Thus, the polynomial in standard form is:

\[ 2x^5 - \frac{1}{7}x^3 - 10x^2 - 8x + 5 \]