Use synthetic division to divide the polynomial \(2x^3 - 5x^2 + 4x - 3\) by the binomial \(x - 2\).
Answer
Step 4: The numbers in the bottom row are the coefficients of the quotient polynomial. The remainder is the last number in this row. So, the quotient polynomial is \(2x^2 - x + 2\) and the remainder is -7.
Step 1 ：Step 1: Write down the coefficients of the polynomial in descending order of their powers, and add a 0 for any missing powers. The coefficients are [2, -5, 4, -3].
Step 2 ：Step 2: Write down the zero that makes the binomial equal to zero, which is 2 in this case.
Step 3 ：Step 3: Perform synthetic division. Bring down the leading coefficient (2) to the bottom row. Multiply it by the zero (2), and write the result under the next coefficient (-5). Add vertically to get the new number in the bottom row (-1). Repeat this process for the remaining coefficients.
Step 4 ：Step 4: The numbers in the bottom row are the coefficients of the quotient polynomial. The remainder is the last number in this row. So, the quotient polynomial is \(2x^2 - x + 2\) and the remainder is -7.
