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To perform long division for x⁷ - 125 ÷ x - 2, follow these steps:

Step 1: Write the dividend (x⁷ - 125) and the divisor (x - 2) in long division format:

_______________________

x - 2 | x⁷ + 0x⁶ + 0x⁵ + 0x⁴ + 0x³ + 0x² + 0x - 125

Step 2: Divide the first term of the dividend (x⁷) by the first term of the divisor (x) to get x⁶. Write this result above the line:

x⁶

_______________________

x - 2 | x⁷ + 0x⁶ + 0x⁵ + 0x⁴ + 0x³ + 0x² + 0x - 125

Step 3: Multiply the divisor (x - 2) by the result (x⁶) and write the product below the dividend, aligning like terms:

x⁶

_______________________

x - 2 | x⁷ + 0x⁶ + 0x⁵ + 0x⁴ + 0x³ + 0x² + 0x - 125

x⁷ - 2x⁶

Step 4: Subtract the product (x⁷ - 2x⁶) from the dividend (x⁷ - 125) and write the result below the line:

x⁶

_______________________

x - 2 | x⁷ + 0x⁶ + 0x⁵ + 0x⁴ + 0x³ + 0x² + 0x - 125

x⁷ - 2x⁶

_____________

2x⁶ + 0x⁵ + 0x⁴ + 0x³ + 0x² + 0x - 125

Step 5: Bring down the next term from the dividend (0x⁵) and write it next to the result:

x⁶

_______________________

x - 2 | x⁷ + 0x⁶ + 0x⁵ + 0x⁴ + 0x³ + 0x² + 0x - 125

x⁷ - 2x⁶

_____________

2x⁶ + 0x⁵ + 0x⁴ + 0x³ + 0x² + 0x - 125

0x⁵

Step 6: Divide the first term of the new dividend (0x⁵) by the first term of the divisor (x) to get 0x⁴. Write this result above the line:

x⁶ + 0x⁴

_______________________

x - 2 | x⁷ + 0x⁶ + 0x⁵ + 0x⁴ + 0x³ + 0x² + 0x - 125

x⁷ - 2x⁶

_____________

2x⁶ + 0x⁵ + 0x⁴ + 0x³ + 0x² + 0x - 125

0x⁵

Step 7: Multiply the divisor (x - 2) by the result (0x⁴) and write the product below the line:

x⁶ + 0x⁴

_______________________

x - 2 | x⁷ + 0x⁶ + 0x⁵ + 0x⁴ + 0x³ + 0x² + 0x - 125

x⁷ - 2x⁶

_____________

2x⁶ + 0x⁵ + 0x⁴ + 0x³ + 0x² + 0x - 125

2x⁶ - 4x⁴

Step 8: Subtract the product (2x⁶ - 4x⁴) from the new dividend (0x⁵) and write the result below the line:

x⁶ + 0x⁴

_______________________

x - 2 | x⁷ + 0x⁶ + 0x⁵ + 0x⁴ + 0x³ + 0x² + 0x - 125

x⁷ - 2x⁶

_____________

2x⁶ + 0x⁵ + 0x⁴ +

Step 1: Write the dividend (x⁷ - 125) and the divisor (x - 2) in long division format:

_______________________

x - 2 | x⁷ + 0x⁶ + 0x⁵ + 0x⁴ + 0x³ + 0x² + 0x - 125

Step 2: Divide the first term of the dividend (x⁷) by the first term of the divisor (x) to get x⁶. Write this result above the line:

x⁶

_______________________

x - 2 | x⁷ + 0x⁶ + 0x⁵ + 0x⁴ + 0x³ + 0x² + 0x - 125

Step 3: Multiply the divisor (x - 2) by the result (x⁶) and write the product below the dividend, aligning like terms:

x⁶

_______________________

x - 2 | x⁷ + 0x⁶ + 0x⁵ + 0x⁴ + 0x³ + 0x² + 0x - 125

x⁷ - 2x⁶

Step 4: Subtract the product (x⁷ - 2x⁶) from the dividend (x⁷ - 125) and write the result below the line:

x⁶

_______________________

x - 2 | x⁷ + 0x⁶ + 0x⁵ + 0x⁴ + 0x³ + 0x² + 0x - 125

x⁷ - 2x⁶

_____________

2x⁶ + 0x⁵ + 0x⁴ + 0x³ + 0x² + 0x - 125

Step 5: Bring down the next term from the dividend (0x⁵) and write it next to the result:

x⁶

_______________________

x - 2 | x⁷ + 0x⁶ + 0x⁵ + 0x⁴ + 0x³ + 0x² + 0x - 125

x⁷ - 2x⁶

_____________

2x⁶ + 0x⁵ + 0x⁴ + 0x³ + 0x² + 0x - 125

0x⁵

Step 6: Divide the first term of the new dividend (0x⁵) by the first term of the divisor (x) to get 0x⁴. Write this result above the line:

x⁶ + 0x⁴

_______________________

x - 2 | x⁷ + 0x⁶ + 0x⁵ + 0x⁴ + 0x³ + 0x² + 0x - 125

x⁷ - 2x⁶

_____________

2x⁶ + 0x⁵ + 0x⁴ + 0x³ + 0x² + 0x - 125

0x⁵

Step 7: Multiply the divisor (x - 2) by the result (0x⁴) and write the product below the line:

x⁶ + 0x⁴

_______________________

x - 2 | x⁷ + 0x⁶ + 0x⁵ + 0x⁴ + 0x³ + 0x² + 0x - 125

x⁷ - 2x⁶

_____________

2x⁶ + 0x⁵ + 0x⁴ + 0x³ + 0x² + 0x - 125

2x⁶ - 4x⁴

Step 8: Subtract the product (2x⁶ - 4x⁴) from the new dividend (0x⁵) and write the result below the line:

x⁶ + 0x⁴

_______________________

x - 2 | x⁷ + 0x⁶ + 0x⁵ + 0x⁴ + 0x³ + 0x² + 0x - 125

x⁷ - 2x⁶

_____________

2x⁶ + 0x⁵ + 0x⁴ +

Koo Kee

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