Question

What is the result when 16x^3 + 8x^2 + 13x - 25 is divided by 4x - 3? If there is a remainder, express the result in the form q(x) + r(x)/(4x - 3).

Answer 1

To divide the polynomial 16x^3 + 8x^2 + 13x - 25 by 4x - 3, you can use synthetic division. The result is 4x^2 + 25x + 82 with a remainder of -25, expressed as q(x) + r(x)/(4x - 3).

Step-by-step explanation:

To divide the polynomial 16x^3 + 8x^2 + 13x - 25 by 4x - 3, we can use synthetic division. Here are the steps:

1. Set up the synthetic division by writing down the coefficients of the polynomial in descending order: 16, 8, 13, -25.
2. Write the divisor in the form of (4x - 3) = 0 and change the sign of the constant term: 4, -3. Place the numbers below the coefficients.
3. Bring down the first coefficient (16) and perform the synthetic division by multiplying 16 by 4 and adding the result to 8. Repeat this step with each coefficient until the end.
4. The final entry in the last row gives the remainder (-25).

Therefore, the result when 16x^3 + 8x^2 + 13x - 25 is divided by 4x - 3 is 4x^2 + 25x + 82 with a remainder of -25. Expressing this in the form q(x) + r(x)/(4x - 3), the division can be written as 4x^2 + 25x + 82 - 25/(4x - 3).