(5x² -17x -15) ÷ (x-4) answer and solution
Answer (1)
Answer:To divide the polynomial (5x² - 17x - 15) by (x - 4), we use polynomial long division. Step 1: Divide the leading term of the dividend (5x²) by the leading term of the divisor (x), which gives 5x.Step 2: Multiply the entire divisor (x - 4) by 5x, resulting in 5x² - 20x.Step 3: Subtract this from the original polynomial:(5x² - 17x - 15) - (5x² - 20x) = (0 + 3x - 15).Step 4: Now, divide the new leading term (3x) by x, which gives 3.Step 5: Multiply the divisor by 3: (x - 4) * 3 = 3x - 12.Step 6: Subtract this from the current polynomial:(3x - 15) - (3x -12) = (0 -3).The quotient is therefore (5x + 3), and the remainder is -3.Thus, the division can be expressed as:(5x² -17x -15) ÷ (x-4) = 5x + 3 + (-3)/(x-4).Step-by-step explanation:
