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
Step 1: Apply the Remainder Theorem. According to the Remainder Theorem, if a polynomial f(x) is divided by (x-a), the remainder is f(a). In this case, f(x) = x^3 + kx^2 - 10x + 16 is divided by (x+1), so a = -1. The remainder is given as 18. Therefore, we set f(-1) = 18. f(-1) = (-1)^3 + k(-1)^2 - 10(-1) + 16 = 18 Step 2: Simplify the equation. Calculate the powers and products. -1 + k(1) + 10 + 16 = 18 -1 + k + 10 + 16 = 18 Step 3: Solve for k. Combine the constant terms on the left side. k + 25 = 18 Subtract 25 from both sides to isolate k. k = 18 - 25 k = -7 The value of k is -7. Send me the next one 📸