Answer :
To determine whether the given polynomial [tex]\(x^5 + 2 x^3 + 6 x + \frac{1}{5}\)[/tex] is in standard form, we should rewrite the polynomial such that the terms are arranged in descending order of the powers of [tex]\(x\)[/tex].
Let's examine the polynomial step-by-step:
1. The given polynomial is: [tex]\(x^5 + 2 x^3 + 6 x + \frac{1}{5}\)[/tex].
2. The highest power of [tex]\(x\)[/tex] is [tex]\(x^5\)[/tex], so it appears first.
3. Next, we have the term with [tex]\(x^3\)[/tex], which is [tex]\(2 x^3\)[/tex].
4. Then comes the [tex]\(x\)[/tex] term, which is [tex]\(6 x\)[/tex].
5. Finally, the constant term, [tex]\(\frac{1}{5}\)[/tex], comes at the end.
When we look at the polynomial [tex]\(x^5 + 2 x^3 + 6 x + \frac{1}{5}\)[/tex], we see that the terms are already arranged in descending order of their powers. Thus, it is in the standard form.
So the correct answer is:
B. It already is in standard form
Let's examine the polynomial step-by-step:
1. The given polynomial is: [tex]\(x^5 + 2 x^3 + 6 x + \frac{1}{5}\)[/tex].
2. The highest power of [tex]\(x\)[/tex] is [tex]\(x^5\)[/tex], so it appears first.
3. Next, we have the term with [tex]\(x^3\)[/tex], which is [tex]\(2 x^3\)[/tex].
4. Then comes the [tex]\(x\)[/tex] term, which is [tex]\(6 x\)[/tex].
5. Finally, the constant term, [tex]\(\frac{1}{5}\)[/tex], comes at the end.
When we look at the polynomial [tex]\(x^5 + 2 x^3 + 6 x + \frac{1}{5}\)[/tex], we see that the terms are already arranged in descending order of their powers. Thus, it is in the standard form.
So the correct answer is:
B. It already is in standard form
