(x⁴- x³ + 2 ) ÷ x + 2​

x³ - 3x² + 6x - 12 __________________________x + 2 | x⁴ - x³ + 2 -(x⁴ + 2x³) ------------------ -3x³ + 2 -(-3x³ - 6x²) ------------------ 6x² + 2 -(6x² + 12x) ------------------ -12x + 2 -(-12x - 24) ------------------ 26- Step 1: Divide the leading term of the dividend (x⁴) by the leading term of the divisor (x), which gives you x³. Write this above the line.- Step 2: Multiply the divisor (x + 2) by the term you just wrote (x³), giving you x⁴ + 2x³. Write this below the dividend and subtract.- Step 3: Bring down the next term (-x³) from the dividend.- Step 4: Repeat the process: Divide the leading term of the new dividend (-3x³) by the leading term of the divisor (x), giving you -3x². Write this above the line. Multiply the divisor (x + 2) by -3x² and subtract.- Step 5: Continue bringing down terms and repeating the process until you reach a remainder that has a lower degree than the divisor. 3. The Result: The result of the division is: - Quotient: x³ - 3x² + 6x - 12- Remainder: 26 Therefore, (x⁴ - x³ + 2) ÷ (x + 2) = x³ - 3x² + 6x - 12 + 26/(x + 2)

Answered by pinoyacoustic57 | 2024-09-07