long division f(x) =4x⁴ +7x³-15x²+6x+18; g(x)=x+3 pls
Answer (1)
Answer:Here's how to perform long division with the given polynomials: 1. Set up the Division: plaintext
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____________x + 3 | 4x⁴ + 7x³ - 15x² + 6x + 18 2. Divide the Leading Terms: - Divide the leading term of the dividend (4x⁴) by the leading term of the divisor (x): 4x⁴ / x = 4x³- Write the result (4x³) above the dividend: plaintext
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4x³ _________x + 3 | 4x⁴ + 7x³ - 15x² + 6x + 18 3. Multiply the Divisor by the Quotient Term: - Multiply the divisor (x + 3) by the quotient term (4x³): (x + 3) * 4x³ = 4x⁴ + 12x³ 4. Subtract: - Subtract the result from the dividend: plaintext
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4x³ _________x + 3 | 4x⁴ + 7x³ - 15x² + 6x + 18 -(4x⁴ + 12x³) ----------------- -5x³ - 15x² 5. Bring Down the Next Term: - Bring down the next term from the dividend (-15x²): plaintext
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4x³ _________x + 3 | 4x⁴ + 7x³ - 15x² + 6x + 18 -(4x⁴ + 12x³) ----------------- -5x³ - 15x² + 6x 6. Repeat Steps 2-5: - Divide the new leading term (-5x³) by the leading term of the divisor (x): -5x³ / x = -5x²- Write the result (-5x²) above the dividend: plaintext
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4x³ - 5x² ______x + 3 | 4x⁴ + 7x³ - 15x² + 6x + 18 -(4x⁴ + 12x³) ----------------- -5x³ - 15x² + 6x - Multiply the divisor (x + 3) by the new quotient term (-5x²): (x + 3) * -5x² = -5x³ - 15x²- Subtract: plaintext
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4x³ - 5x² ______x + 3 | 4x⁴ + 7x³ - 15x² + 6x + 18 -(4x⁴ + 12x³) ----------------- -5x³ - 15x² + 6x -(-5x³ - 15x²) ----------------- 6x + 18 - Bring down the next term (+18): plaintext
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4x³ - 5x² ______x + 3 | 4x⁴ + 7x³ - 15x² + 6x + 18 -(4x⁴ + 12x³) ----------------- -5x³ - 15x² + 6x -(-5x³ - 15x²) ----------------- 6x + 18 7. Final Steps: - Divide the new leading term (6x) by the leading term of the divisor (x): 6x / x = 6- Write the result (6) above the dividend: plaintext
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4x³ - 5x² + 6 ____x + 3 | 4x⁴ + 7x³ - 15x² + 6x + 18 -(4x⁴ + 12x³) ----------------- -5x³ - 15x² + 6x -(-5x³ - 15x²) ----------------- 6x + 18 - Multiply the divisor (x + 3) by the new quotient term (6): (x + 3) * 6 = 6x + 18- Subtract: plaintext
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4x³ - 5x² + 6 ____x + 3 | 4x⁴ + 7x³ - 15x² + 6x + 1
