Final answer:
The result of dividing 16x^3 + 20x^2 + 10x + 3 by 4x + 3 is 4x^2 + 2x + 1.
Step-by-step explanation:
To divide the polynomial 16x^3 + 20x^2 + 10x + 3 by the binomial 4x + 3, we can use long division. The first step is to divide 16x^3 by 4x, which gives us 4x^2. We then multiply 4x + 3 by 4x^2 to get 16x^3 + 12x^2. Subtracting this from the original polynomial gives us 8x^2 + 10x + 3. We then divide 8x^2 by 4x, which gives us 2x. We proceed to multiply 4x + 3 by 2x to get 8x^2 + 6x. Subtracting this from the remaining polynomial gives us 4x + 3. Since 4x + 3 is a factor of the original polynomial, there is no remainder. Therefore, the result of the division is 4x^2 + 2x + 1.