Question

Divide each of the following polyr (4x³ -8x²+3x-1)-:(2x+1)

Answer 1

To divide the polynomial (4x³ - 8x² + 3x - 1) by (2x + 1), we can use long division. The result of the division is 2x² - 5x + 4 with a remainder of -5.

Step-by-step explanation:

To divide the polynomial (4x³ - 8x² + 3x - 1) by (2x + 1), we can use long division. Here's how:

1. First, divide the leading term of the polynomial (4x³) by the leading term of the divisor (2x), which gives us 2x².
2. Multiply the entire divisor (2x + 1) by 2x², which gives us 4x³ + 2x².
3. Subtract this result from the original polynomial (4x³ - 8x² + 3x - 1) to get -10x² + 3x - 1.
4. Repeat this process with the new polynomial -10x² + 3x - 1.
5. Divide the leading term of the new polynomial (-10x²) by the leading term of the divisor (2x), which gives us -5x.
6. Multiply the entire divisor (2x + 1) by -5x, which gives us -10x² - 5x.
7. Subtract this result from the new polynomial (-10x² + 3x - 1) to get 8x - 1.
8. Finally, divide the remaining polynomial term (8x) by the leading term of the divisor (2x), which gives us 4.
9. Multiply the entire divisor (2x + 1) by 4, which gives us 8x + 4.
10. Subtract this result from the remaining polynomial (8x - 1) to get -5.

Therefore, the result of the division is 2x² - 5x + 4 with a remainder of -5.