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: Identify the polynomial and the divisor. The polynomial is P(x) = 3x^3 + 6x - 1. The divisor is x - 3. Step 2: Apply the Remainder Theorem. According to the Remainder Theorem, if a polynomial P(x) is divided by x - c, the remainder is P(c). In this case, c = 3. So, we need to find P(3). Step 3: Substitute x = 3 into the polynomial. P(3) = 3(3)^3 + 6(3) - 1 Step 4: Calculate the value. P(3) = 3(27) + 18 - 1 P(3) = 81 + 18 - 1 P(3) = 99 - 1 P(3) = 98 The remainder is 98. The final answer is 98.