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Combine like terms:

[tex]\[ z^5 + 8z^4 + z^2 \][/tex]

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The simplified polynomial is [tex]$\square$[/tex].

B. The polynomial cannot be simplified.

Sagot :

GinnyAnswer
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.
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