Final answer:
The factor of the given expression 7z^4 - 5+10(y + 2) is option C, 10(y + 2), which is directly part of the original expression.
Step-by-step explanation:
The student is asking which of the provided options is a factor of the given expression 7z^4 - 5+10(y + 2). A factor of an expression is a quantity that divides into the expression without leaving a remainder. To determine if something is a factor, we look for terms or expressions that can be factored out or which multiply with another expression to give the original expression.
In the presented options, option C, 10(y + 2), is indeed a factor. This is because it directly multiplies by 1 in the expression, and no factoring or manipulation is needed to see it is part of the original expression. The given expression already has a "10(y + 2)" component which means it directly contributes to forming the given expression without requiring any additional modification.
Options A, B, and D are not factors of the given expression. Option A is not present in the expression, option B lacks the term '10(y + 2)', and option D has an incorrect variable 'g' compared to the original.