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. The Remainder Theorem states that if a polynomial P(x) is divided by x-a, the remainder is P(a). Given P(x) = x^2 + bx + 2 and the divisor is x+3, which means a = -3. The remainder is 5. Therefore, we can write: P(-3) = 5 Step 2: Substitute x = -3 into the polynomial. Substitute x = -3 into P(x) and set the expression equal to the remainder: (-3)^2 + b(-3) + 2 = 5 Step 3: Simplify the equation. Calculate the square and the product: 9 - 3b + 2 = 5 Step 4: Solve for b. Combine the constant terms and isolate b: 11 - 3b = 5 -3b = 5 - 11 -3b = -6 b = (-6)/(-3) b = 2 The value of b is 2. Send me the next one 📸