High School

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ What is the remainder in the synthetic division problem below?

[tex]
\[
\begin{array}{|ccc}
1 & 2 & -3 \\
\hline
\end{array}
\]
[/tex]

A. 3
B. 5
C. 6
D. 4

Answer :

To find the remainder in the given synthetic division problem, we follow these steps:

1. Identify the Polynomial and Divisor: We are given the coefficients [tex]\([1, 2, -3]\)[/tex], which correspond to the polynomial [tex]\(x^2 + 2x - 3\)[/tex].

2. Set Up for Synthetic Division: We are dividing by [tex]\(x - 1\)[/tex], which means the divisor term is 1. This is because synthetic division uses the root of the divisor when setting up the calculation.

3. Perform the Synthetic Division:
- Write the first coefficient [tex]\(1\)[/tex] in the result row.
- Multiply this result by the divisor term (1) and add the next coefficient (2):
- [tex]\(1 \times 1 + 2 = 3\)[/tex]. Write [tex]\(3\)[/tex] in the result row.
- Repeat this process: Multiply the last result [tex]\(3\)[/tex] by the divisor term (1) and add the last coefficient (-3):
- [tex]\(3 \times 1 - 3 = 0\)[/tex]. Write [tex]\(0\)[/tex] in the result row.

4. Interpret the Result: The sequence of numbers in the result, [tex]\([1, 3, 0]\)[/tex], gives us the quotient and the remainder. The remainder of the division is the last number in the sequence, which is [tex]\(0\)[/tex].

Therefore, the remainder of the synthetic division is [tex]\(0\)[/tex].