Answer :
We start with the polynomial
$$6x^3 - 8x^5 + 2 + 9x^7 - 4x.$$
**Step 1. Identify the terms and their exponents.**
The terms in the polynomial are:
- \(6x^3\) (the exponent is \(3\))
- \(-8x^5\) (the exponent is \(5\))
- \(2\) (this is a constant term, so the exponent is \(0\))
- \(9x^7\) (the exponent is \(7\))
- \(-4x\) (the exponent is \(1\))
**Step 2. Arrange the terms in descending order of exponents.**
The exponents in descending order are:
\[
7, \ 5, \ 3, \ 1, \ 0.
\]
So the corresponding terms are:
- \(9x^7\) (exponent \(7\))
- \(-8x^5\) (exponent \(5\))
- \(6x^3\) (exponent \(3\))
- \(-4x\) (exponent \(1\))
- \(2\) (exponent \(0\))
**Step 3. Write the polynomial with terms arranged in descending powers of \(x\).**
Thus, the final expression is:
$$\boxed{9x^7 - 8x^5 + 6x^3 - 4x + 2.}$$
$$6x^3 - 8x^5 + 2 + 9x^7 - 4x.$$
**Step 1. Identify the terms and their exponents.**
The terms in the polynomial are:
- \(6x^3\) (the exponent is \(3\))
- \(-8x^5\) (the exponent is \(5\))
- \(2\) (this is a constant term, so the exponent is \(0\))
- \(9x^7\) (the exponent is \(7\))
- \(-4x\) (the exponent is \(1\))
**Step 2. Arrange the terms in descending order of exponents.**
The exponents in descending order are:
\[
7, \ 5, \ 3, \ 1, \ 0.
\]
So the corresponding terms are:
- \(9x^7\) (exponent \(7\))
- \(-8x^5\) (exponent \(5\))
- \(6x^3\) (exponent \(3\))
- \(-4x\) (exponent \(1\))
- \(2\) (exponent \(0\))
**Step 3. Write the polynomial with terms arranged in descending powers of \(x\).**
Thus, the final expression is:
$$\boxed{9x^7 - 8x^5 + 6x^3 - 4x + 2.}$$
