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
Fresh day 💕AHDWOAH, let's solve. To use synthetic division for 3x^3 - 5x^2 + 3 divided by (x-3): Step 1: Set up the synthetic division. The divisor is (x-3), so we use 3 for the division. The coefficients of the polynomial 3x^3 - 5x^2 + 0x + 3 are 3, -5, 0, 3. (Note: A 0 is used for the missing x term). c|cccc 3 & 3 & -5 & 0 & 3 \\ & & & & \\ & & & & Step 2: Perform the synthetic division. Bring down the first coefficient (3). Multiply 3 × 3 = 9. Add to -5: -5 + 9 = 4. Multiply 4 × 3 = 12. Add to 0: 0 + 12 = 12. Multiply 12 × 3 = 36. Add to 3: 3 + 36 = 39. c|cccc 3 & 3 & -5 & 0 & 3 \\ & & 9 & 12 & 36 \\ & 3 & 4 & 12 & 39 Step 3: Identify the quotient and the remainder. The numbers in the bottom row, excluding the last one, are the coefficients of the quotient. Since the original polynomial was degree 3, the quotient will be degree 2. The last number is the remainder. The coefficients of the quotient are 3, 4, 12. The quotient is 3x^2 + 4x + 12. The remainder is 39. The quotient is 3x^2 + 4x + 12 The remainder is 39 Send me the next one 📸