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]\[
1 \longdiv 4 \quad 6 \quad -1
\][/tex]

A. 3
B. 7
C. 9
D. 5

Answer :

Sure! Let's go through the synthetic division process step by step to find the remainder.

We are performing synthetic division for the polynomial represented by the coefficients [tex]\(4, 6, -1\)[/tex] using the divisor [tex]\(x - 1\)[/tex], where 1 is the number you’ll be working with in the synthetic division. The steps are as follows:

1. Write Down the Coefficients: Start by writing the coefficients of the polynomial, which are [tex]\(4, 6, -1\)[/tex].

2. Bring Down the First Coefficient: Bring down the first coefficient, [tex]\(4\)[/tex]. This is the first part of our result.

3. Multiply and Add:
- Multiply the number you brought down (4) by the divisor (1). [tex]\(4 \times 1 = 4\)[/tex].
- Add this result to the next coefficient (6). [tex]\(6 + 4 = 10\)[/tex].

4. Repeat Multiply and Add:
- Now, take the result from the previous addition (10), multiply it by the divisor (1). [tex]\(10 \times 1 = 10\)[/tex].
- Add this result to the next coefficient (-1). [tex]\(-1 + 10 = 9\)[/tex].

5. Result:
- The number [tex]\(9\)[/tex] you get as a result of the last addition is the remainder of the division.

Thus, the remainder of the synthetic division is [tex]\(9\)[/tex].

So, the correct answer is [tex]\(C. 9\)[/tex].