Final answer:
To divide -45x⁴ + 36x³ - 15x² - 3x + 16 by 5x - 4, use long division.
Step-by-step explanation:
To divide the polynomial -45x⁴ + 36x³ - 15x² - 3x + 16 by 5x - 4, we can use long division.
- Start by dividing the first term of the numerator (-45x⁴) by the first term of the denominator (5x). The result is -9x³.
- Multiply the denominator (5x - 4) by the result (-9x³) and subtract it from the numerator (-45x⁴ + 36x³ - 15x² - 3x + 16).
- Continuing this process, divide the new numerator by the denominator and repeat the steps until there are no more terms to divide.
The quotient is -9x³ + 21x² + 0x - 3 and the remainder is 28. Therefore, the division of -45x⁴ + 36x³ - 15x² - 3x + 16 by 5x - 4 is -9x³ + 21x² - 3 with a remainder of 28.