To rewrite the polynomial expression [tex]\( 35 x^3 + 22 x^5 - 4 x^4 - 3 x^2 - 5 \)[/tex] in standard form, we need to arrange the terms in descending order of their powers. Here’s a step-by-step process to achieve this:
1. Identify the powers of [tex]\( x \)[/tex] in each term:
- [tex]\( 35 x^3 \)[/tex] has a power of 3.
- [tex]\( 22 x^5 \)[/tex] has a power of 5.
- [tex]\( -4 x^4 \)[/tex] has a power of 4.
- [tex]\( -3 x^2 \)[/tex] has a power of 2.
- [tex]\( -5 \)[/tex] has a power of 0 (constant term).
2. Arrange these terms in order from the highest power of [tex]\( x \)[/tex] to the lowest:
- The highest power is [tex]\( 22 x^5 \)[/tex].
- The next highest power is [tex]\( -4 x^4 \)[/tex].
- Following is [tex]\( 35 x^3 \)[/tex].
- Then [tex]\( -3 x^2 \)[/tex].
- Finally, the constant term [tex]\( -5 \)[/tex].
3. Combine these ordered terms to form the polynomial in standard form:
[tex]\[
22 x^5 - 4 x^4 + 35 x^3 - 3 x^2 - 5
\][/tex]
Comparing this result with the provided options, we see that it matches:
C. [tex]\( 22 x^5 - 4 x^4 + 35 x^3 - 3 x^2 - 5 \)[/tex]
Hence, the correct standard form of the given expression is:
C. [tex]\( 22 x^5 - 4 x^4 + 35 x^3 - 3 x^2 - 5 \)[/tex]
