To determine which option is a factor of the given expression [tex]\(5z^4 - 3 + 8(y^3 + 10)\)[/tex], let's start by understanding what a factor is. A factor of an expression is a term that, when multiplied by another term, gives the original expression or part of the expression.
Let's examine the given expression and the options:
Expression:
[tex]\[5z^4 - 3 + 8(y^3 + 10)\][/tex]
### Option A: [tex]\(\left(y^3 + 10\right)\)[/tex]
We need to check if [tex]\(\left(y^3 + 10\right)\)[/tex] is a factor. If we consider [tex]\(\left(y^3 + 10\right)\)[/tex], multiplying it by 8 yields [tex]\(8(y^3 + 10)\)[/tex], which is part of our original expression.
### Option B: [tex]\(8\left(y^3 + 10\right)\)[/tex]
This means multiplying the factor [tex]\(\left(y^3 + 10\right)\)[/tex] by 8, which directly gives the term [tex]\(8(y^3 + 10)\)[/tex] in the expression.
### Option C: [tex]\(-3 + 8\left(y^3 + 10\right)\)[/tex]
Let's check if [tex]\(-3 + 8(y^3 + 10)\)[/tex] is a factor. The term [tex]\(-3 + 8(y^3 + 10)\)[/tex] cannot be exactly factored out from the entire expression as it includes additional constants and multiplications.
### Option D: [tex]\(5z^4 - 3\)[/tex]
Checking [tex]\(5z^4 - 3\)[/tex], we observe that this term is part of the original expression, but it does not appear to be a standalone factor that can be multiplied with another term to get the entire original expression.
By analyzing all the terms and options carefully, the factor in the original given expression [tex]\(5z^4 - 3 + 8(y^3 + 10)\)[/tex] is clearly:
### Answer:
B. [tex]\(8\left(y^3 + 10\right)\)[/tex]
