This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Another day — let's solve it. Step 1: Identify the polynomial and the divisor. The polynomial is f(x) = x^4 - 2x^3 - 6x^2 - 2x + 1. The divisor is x+2. Step 2: Apply the Remainder Theorem. The Remainder Theorem states that if a polynomial f(x) is divided by x-a, the remainder is f(a). In this case, the divisor is x+2, which can be written as x - (-2). So, a = -2. Therefore, the remainder is f(-2). Step 3: Substitute x = -2 into the polynomial f(x). f(-2) = (-2)^4 - 2(-2)^3 - 6(-2)^2 - 2(-2) + 1 Step 4: Calculate each term. (-2)^4 = 16 -2(-2)^3 = -2(-8) = 16 -6(-2)^2 = -6(4) = -24 -2(-2) = 4 +1 Step 5: Sum the calculated terms to find the remainder. f(-2) = 16 + 16 - 24 + 4 + 1 f(-2) = 32 - 24 + 4 + 1 f(-2) = 8 + 4 + 1 f(-2) = 13 The remainder is 13. The final answer is 13. Send me the next one 📸