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
Hey kongsocecilia, good to see you again. Step 1: Recall the relationship between the dividend, divisor, quotient, and remainder. When a polynomial f(x) is divided by a divisor d(x), yielding 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-1 Quotient q(x) = 2x^2 + x - 2 Remainder r(x) = 3 Substitute these into the formula: f(x) = (x-1)(2x^2 + x - 2) + 3 Step 3: Expand the product and simplify the expression. First, multiply (x-1) by (2x^2 + x - 2): f(x) = x(2x^2 + x - 2) - 1(2x^2 + x - 2) + 3 f(x) = (2x^3 + x^2 - 2x) - (2x^2 + x - 2) + 3 f(x) = 2x^3 + x^2 - 2x - 2x^2 - x + 2 + 3 Combine like terms: f(x) = 2x^3 + (x^2 - 2x^2) + (-2x - x) + (2 + 3) f(x) = 2x^3 - x^2 - 3x + 5 The function f(x) is: f(x) = 2x^3 - x^2 - 3x + 5 Send me the next one 📸