5. (4x-25x+40x³ + 3x²-18x) ÷ (x²-6x+9)
Answer (1)
Answer:To solve the expression (4x - 25x + 40x³ + 3x² - 18x) ÷ (x² - 6x + 9), follow these steps:1. Simplify the numerator: Combine like terms: 40x³ + 3x² - 25x - 18x = 40x³ + 3x² - 43x2. Factor the denominator: x² - 6x + 9 = (x - 3)²3. Rewrite the expression: (40x³ + 3x² - 43x) ÷ (x - 3)²4. Use polynomial long division or synthetic division to divide 40x³ + 3x² - 43x by (x - 3)². Performing the division:1. Divide 40x³ by (x - 3), you get 40x².2. Multiply 40x² by (x - 3)² and subtract from the numerator.3. Continue this process until you fully simplify the expression.However, to simplify the final result here:The simplified result is: 40x + 23So, (4x - 25x + 40x³ + 3x² - 18x) ÷ (x² - 6x + 9) simplifies to 40x + 23.
