Final Answer:
The result of dividing (4x³ - 3x² + 6x + 20) by (4x + 5) is (x² - 2x + 4) with a remainder of 0.
Step-by-step explanation:
To find the result of dividing the polynomial (4x³ - 3x² + 6x + 20) by the binomial (4x + 5), polynomial long division or synthetic division can be used. Dividing (4x³ - 3x² + 6x + 20) by (4x + 5) yields a quotient of (x² - 2x + 4) and a remainder of 0.
The process of polynomial long division involves dividing the highest degree term of the dividend by the highest degree term of the divisor, which gives the first term of the quotient. After multiplying the divisor by this term and subtracting the result from the dividend, the process continues until the remainder has a lower degree than the divisor. In this case, the remainder is 0, indicating that the divisor (4x + 5) divides the polynomial (4x³ - 3x² + 6x + 20) evenly.
Therefore, the result of the division is the quotient (x² - 2x + 4) with no remainder, signifying that (4x³ - 3x² + 6x + 20) is evenly divisible by (4x + 5).