Answer :
Sure, let's solve this step-by-step using synthetic division.
We need to divide the polynomial [tex]\(4x^2 + 6x - 1\)[/tex] by [tex]\(x - 1\)[/tex] and find the remainder.
Here's how we do it:
1. Identify the divisor and the root: Since the divisor is [tex]\(x - 1\)[/tex], the root is [tex]\(r = 1\)[/tex].
2. Write down the coefficients: The coefficients of the polynomial [tex]\(4x^2 + 6x - 1\)[/tex] are 4, 6, and -1.
3. Set up synthetic division:
- Write the root [tex]\(r = 1\)[/tex] to the left.
- Write the coefficients [tex]\([4, 6, -1]\)[/tex] to the right.
4. Begin the synthetic division process:
- Bring down the first coefficient (4) to start. This is your initial value.
- Multiply this value (4) by the root (1) and write the result (4) underneath the second coefficient (6).
- Add 6 and 4 to get 10. Write this result under the line.
- Multiply the new value (10) by the root (1) and write the result (10) underneath the third coefficient (-1).
- Add -1 and 10 to get 9.
The last number we get from this process (9) is the remainder.
So, the remainder when [tex]\(4x^2 + 6x - 1\)[/tex] is divided by [tex]\(x - 1\)[/tex] is 9.
Therefore, the answer is:
C. 9
We need to divide the polynomial [tex]\(4x^2 + 6x - 1\)[/tex] by [tex]\(x - 1\)[/tex] and find the remainder.
Here's how we do it:
1. Identify the divisor and the root: Since the divisor is [tex]\(x - 1\)[/tex], the root is [tex]\(r = 1\)[/tex].
2. Write down the coefficients: The coefficients of the polynomial [tex]\(4x^2 + 6x - 1\)[/tex] are 4, 6, and -1.
3. Set up synthetic division:
- Write the root [tex]\(r = 1\)[/tex] to the left.
- Write the coefficients [tex]\([4, 6, -1]\)[/tex] to the right.
4. Begin the synthetic division process:
- Bring down the first coefficient (4) to start. This is your initial value.
- Multiply this value (4) by the root (1) and write the result (4) underneath the second coefficient (6).
- Add 6 and 4 to get 10. Write this result under the line.
- Multiply the new value (10) by the root (1) and write the result (10) underneath the third coefficient (-1).
- Add -1 and 10 to get 9.
The last number we get from this process (9) is the remainder.
So, the remainder when [tex]\(4x^2 + 6x - 1\)[/tex] is divided by [tex]\(x - 1\)[/tex] is 9.
Therefore, the answer is:
C. 9
