Question

Rewrite the following polynomial in standard form.
1-4x+ x^5/9-x^4

Answer 1

To rewrite the polynomial in standard form, we arrange the terms in descending order of their powers, combine like terms if necessary, and write down the constant term last, resulting in the polynomial x^5/9 - x^4 - 4x + 1.

Step-by-step explanation:

The student is asked to rewrite a polynomial in standard form. The polynomial given is 1 - 4x + (x^5/9) - x^4. To put it in standard form, we need to arrange the terms in descending order of their degree (the exponent on the x term). The standard form should thus start with the highest degree term and end with the constant term.

The given polynomial already has terms arranged from highest degree to lowest: x^5, x^4, x, and the constant term. Let's combine like terms and express the polynomial in standard form:

1. First, write down the term with the highest power, which is x^5/9.
2. Next, place the terms in descending order of their powers of x. If a term has a fraction, it should be expressed as such.
3. Combine any like terms, if necessary.
4. Write down the constant term last.

The polynomial in standard form would be:

x^5/9 - x^4 - 4x + 1.