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
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 polynomial 3x^3 - 5x^2 + 3 is missing an x term, so we write it as 3x^3 - 5x^2 + 0x + 3. The coefficients are 3, -5, 0, 3. c|cccc 3 & 3 & -5 & 0 & 3 \\ & & & & \\ & & & & Step 2: Perform the synthetic division. Bring down the first coefficient, 3. Multiply 3 by the divisor 3 to get 9. Add 9 to -5 to get 4. Multiply 4 by the divisor 3 to get 12. Add 12 to 0 to get 12. Multiply 12 by the divisor 3 to get 36. Add 36 to 3 to get 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 and we divided by a degree 1 polynomial, the quotient will be degree 2. The last number in the bottom row 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 That's 2 down. 3 left today — send the next one.