Question

Fill in the missing values below to find the quotient when 3x³ + 5x² + 6x - 16 is divided by

3x - 4. If there is a remainder, express the result in the form q(a) + r(x)/b(x). Note: you may not need to use all the boxes.

Answer
(3x³ + 5x² + 6x - 16) ÷ (3x − 4) = ____

Answer 1

To find the quotient when 3x³ + 5x² + 6x - 16 is divided by 3x - 4, you can use polynomial long division. The quotient is x² + 3x and the remainder is 18x - 16. Therefore, the result is x² + 3x + (18x - 16) / (3x - 4).

Step-by-step explanation:

To find the quotient when 3x³ + 5x² + 6x - 16 is divided by 3x - 4, we can use polynomial long division. Here are the steps:

1. Arrange the dividend (3x³ + 5x² + 6x - 16) and the divisor (3x - 4) in descending order of powers of x.
2. Divide the first term of the dividend (3x³) by the first term of the divisor (3x) to get x² as the first term of the quotient.
3. Multiply the divisor (3x - 4) by x² to get 3x³ - 4x².
4. Subtract this result from the dividend to get (3x³ + 5x² + 6x - 16) - (3x³ - 4x²) = 9x² + 6x - 16.
5. Repeat the process with the new dividend (9x² + 6x - 16) and the divisor (3x - 4).
6. Divide the first term of the new dividend (9x²) by the first term of the divisor (3x) to get 3x as the next term of the quotient.
7. Multiply the divisor (3x - 4) by 3x to get 9x² - 12x.
8. Subtract this result from the new dividend (9x² + 6x - 16) to get (9x² + 6x - 16) - (9x² - 12x) = 18x - 16.

We cannot continue with the division because the degree of the new dividend (18x - 16) is lower than the degree of the divisor (3x - 4). Therefore, the quotient is x² + 3x and the remainder is 18x - 16. Thus, the result is x² + 3x + (18x - 16) / (3x - 4).