Question

divide 8m³+8m²+4m+1 by 1+2m​

Answer 1

Answer:

To divide the polynomial (8m³ + 8m² + 4m + 1) by (1 + 2m), we can use polynomial long division. The process involves dividing the highest degree term of the dividend by the highest degree term of the divisor and then proceeding with the division of subsequent terms. Here's how it looks:

4m^2 - 8m + 20

_______________________

1 + 2m | 8m^3 + 8m^2 + 4m + 1

Step 1: Divide (8m³) by (1+2m) to get 8m².

Step 2: Multiply (1+2m) by 8m² to get (8m^2 + 16m²) and write it below the corresponding terms.

Step 3: Subtract (8m² + 16m²) from (8m² + 8m²) to get 0m², and write it below the horizontal line.

Step 4: Bring down the next term, which is 4m.

Step 5: Divide (0m² + 4m) by (1+2m) to get 4.

Step 6: Multiply (1+2m) by 4 to get (4 + 8m) and write it below the corresponding terms.

Step 7: Subtract (4 + 8m) from (4m + 4) to get -8m, and write it below the horizontal line.

Step 8: Bring down the last term, which is 1.

Step 9: Divide (-8m + 1) by (1+2m) to get -4.

Step 10: Multiply (1+2m) by -4 to get (-4 - 8m) and write it below the corresponding terms.

Step 11: Subtract (-4 - 8m) from (-8m + 1) to get 5, which is the remainder.

Therefore, the result of the division is:

Quotient: 4m^2 - 8m + 4

Remainder: 5

So, (8m³ + 8m² + 4m + 1) divided by (1 + 2m) is equal to 4m^2 - 8m + 4 with a remainder of 5.