Question

Use the long division method to find the result when 8x4 - 4x3 – 30x2 + 9x + 19 is divided by 4x2 – 3. ​

Answer 1

To divide 8x4 - 4x3 – 30x2 + 9x + 19 by 4x2 - 3 using the long division method, follow these steps: divide, multiply, subtract, repeat.

Step-by-step explanation:

To divide 8x4 - 4x3 – 30x2 + 9x + 19 by 4x2 - 3 using the long division method, follow these steps:

1. Divide the first term of the dividend by the first term of the divisor: 8x4 ÷ 4x2 = 2x2.
2. Multiply the entire divisor by the quotient obtained in the previous step: (2x2) * (4x2 - 3) = 8x4 - 6x2.
3. Subtract the result from the original dividend: (8x4 - 4x3 – 30x2 + 9x + 19) - (8x4 - 6x2) = -4x3 - 30x2 + 9x + 19 - (-6x2) = -4x3 - 24x2 + 9x + 19.
4. Repeat these steps until you have no more terms to bring down.

The final result is -4x3 - 24x2 + 9x + 19 with no remaining terms to bring down.