Certainly! Let's solve the given problem step-by-step.
The expression in question is:
[tex]\[ 7z^4 - 5 + 10(y^3 + 2) \][/tex]
We need to find which of the given choices is a factor of this expression.
1. Analyze the expression:
Let's rewrite the given expression in a clearer form:
[tex]\[
7z^4 - 5 + 10(y^3 + 2)
\][/tex]
Firstly, observe that [tex]\( 10(y^3 + 2) \)[/tex] is a separate term on its own summarized within the given expression.
2. Identifying a common term:
Look at the term [tex]\( 10(y^3 + 2) \)[/tex]. This indicates that [tex]\( (y^3 + 2) \)[/tex] is bundled within a multiplication by 10. So, if we need to identify separate terms or factors in the expression, [tex]\( y^3 + 2 \)[/tex] on its own is a logical focus.
3. Check each option:
- Option A: [tex]\( 10(y^3 + 2) \)[/tex]:
This suggests the whole term multiplied together which is indeed part of the expression, but not a basic factor.
- Option B: [tex]\( 7z^4 - 5 \)[/tex]:
This part of the expression is actually separated by addition from [tex]\( 10(y^3 + 2) \)[/tex], so it isn't a common factor.
- Option C: [tex]\( -5 + 10(y^3 + 2) \)[/tex]:
This again combines separate components of the expression together but doesn't serve as a basic common factor.
- Option D: [tex]\( y^3 + 2 \)[/tex]:
This term appears distinctly within [tex]\( 10(y^3 + 2) \)[/tex]. This indicates that [tex]\( y^3 + 2 \)[/tex] is a particular structure repeatedly involved in the overall expression, suggesting it is a basic component.
After this careful examination, we can clearly see that the expression includes [tex]\( y^3 + 2 \)[/tex] as an identifiable independent term, meaning [tex]\( y^3 + 2 \)[/tex] is indeed a factor of the entire expression.
Thus, the correct choice is:
[tex]\[ D. \left(y^3+2\right) \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{4} \][/tex]
