To write a polynomial in standard form, we need to arrange the terms in descending order of the exponents of [tex]\( x \)[/tex].
Let's examine the given polynomial:
[tex]\[ x^5 + 2x^3 + 6x + \frac{1}{5} \][/tex]
Here are the steps to write it in standard form:
1. Identify the term with the highest exponent. In this case, it is [tex]\( x^5 \)[/tex].
2. Arrange the remaining terms in descending order of their exponents. The order should be:
- [tex]\( x^5 \)[/tex]
- [tex]\( 2x^3 \)[/tex]
- [tex]\( 6x \)[/tex] (which is [tex]\( 6x^1 \)[/tex], although we typically don't write the 1)
- The constant term [tex]\( \frac{1}{5} \)[/tex] (which is [tex]\( 6x^0 \)[/tex], although we typically don't write the 0)
So, the polynomial rewritten in standard form is:
[tex]\[ x^5 + 2x^3 + 6x + \frac{1}{5} \][/tex]
From the given options:
A. It already is in standard form
B. [tex]\( 6x + 2x^3 + x^5 + \frac{1}{5} \)[/tex]
C. [tex]\( \frac{1}{5} + 6x + 0x^2 + 2x^3 + x^5 \)[/tex]
D. [tex]\( 6x + 2x^3 + x^5 + \frac{1}{5} + 0x^2 \)[/tex]
Only option A correctly represents the polynomial in its standard form. Therefore, the correct answer is:
A. It already is in standard form
