Final answer:
To determine the factor of 5x³ − 135, use long division to divide the expression by each option and check for a remainder of zero.
Step-by-step explanation:
To determine which of the options is a factor of the expression 5x³ − 135, we can use long division. We divide 5x³ − 135 by each option and check if the remainder is equal to zero. If the remainder is zero, then the option is a factor.
Let's start with option d. We divide 5x³ − 135 by x - 5:
- Divide the first term, 5x³, by x: 5x²
- Multiply the divisor, x - 5, by the quotient, 5x²: (x - 5)(5x²) = 5x³ - 25x²
- Subtract the result from the original expression: 5x³ - 135 - (5x³ - 25x²) = -135 + 25x²
- Check if the result is equal to zero. In this case, -135 + 25x² ≠ 0, so x - 5 is not a factor of 5x³ − 135.
We can repeat this process for options a, b, and c to determine which option is a factor.