To combine like terms, we need to identify the terms in the polynomial that have the same variable raised to the same power.
Let's look at the given polynomial:
[tex]\[ z^5 + 8z^4 + z^2 \][/tex]
1. Identify like terms:
- [tex]\( z^5 \)[/tex] has the variable [tex]\( z \)[/tex] raised to the power of 5.
- [tex]\( 8z^4 \)[/tex] has the variable [tex]\( z \)[/tex] raised to the power of 4.
- [tex]\( z^2 \)[/tex] has the variable [tex]\( z \)[/tex] raised to the power of 2.
2. Analyze the exponents:
- Notice that each term has a different exponent. [tex]\( z^5 \)[/tex], [tex]\( 8z^4 \)[/tex], and [tex]\( z^2 \)[/tex] have exponents of 5, 4, and 2, respectively.
- Unlike terms cannot be combined because combining requires the terms to have the same exact variable raised to the same power.
3. Combine like terms:
- Since [tex]\( z^5 \)[/tex], [tex]\( 8z^4 \)[/tex], and [tex]\( z^2 \)[/tex] do not have the same exponent, they are not like terms and thus cannot be combined.
So, the correct answer is:
B. The polynomial cannot be simplified.
