Final answer:
The correct factor of 3xy³ - 5x - 5 is x².Therefore, the correct answer is c) x²,
Step-by-step explanation:
To find a factor of the expression 3xy³ - 5x - 5, we need to see which option is a factor when substituted into the expression. Let's check each option:
a) ax: Substituting ax into the expression gives us 3a(xy³) - 5(ax) - 5. This does not match the original expression, so it is not a factor.
b) 2x + 1: Substituting 2x + 1 into the expression gives us 3(2x + 1)y³ - 5(2x + 1) - 5. This does not match the original expression, so it is not a factor.
c) x²: Substituting x² into the expression gives us 3(xy³)² - 5x - 5. This matches the original expression, so x² is a factor.
d) 2x + 2: Substituting 2x + 2 into the expression gives us 3(2x + 2)y³ - 5(2x + 2) - 5. This does not match the original expression, so it is not a factor.
Therefore, the correct answer is c) x², which is a factor of 3xy³ - 5x - 5.