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
Welcome back Mhiz — missed you this week. Step 1: Recall the relationship between the dividend, divisor, quotient, and remainder. When a polynomial f(x) is divided by a divisor D(x), resulting in a quotient Q(x) and a remainder R(x), the relationship is given by: f(x) = D(x) · Q(x) + R(x) Step 2: Substitute the given values into the formula. Given: Divisor D(x) = x+2 Quotient Q(x) = x^2+x-1 Remainder R(x) = 3 Substitute these into the formula: f(x) = (x+2)(x^2+x-1) + 3 Step 3: Expand the product of the divisor and quotient. Multiply (x+2) by (x^2+x-1): f(x) = x(x^2+x-1) + 2(x^2+x-1) + 3 f(x) = (x^3+x^2-x) + (2x^2+2x-2) + 3 Step 4: Combine like terms to find f(x). f(x) = x^3 + (x^2+2x^2) + (-x+2x) + (-2+3) f(x) = x^3 + 3x^2 + x + 1 The polynomial f(x) is: f(x) = x^3 + 3x^2 + x + 1 Send me the next one 📸