Answer :
To find the remainder when using synthetic division, follow these steps:
1. Identify the root: Since the divisor is given as [tex]\( x - 4 \)[/tex], the root is 4.
2. Write down the coefficients: For the polynomial described, the coefficients are 1, 6, and -1.
3. Begin synthetic division:
- Start with the first coefficient, which is 1.
- Multiply this number by the root (4) and add the result to the next coefficient.
4. Perform the calculations step-by-step:
- Start with the first coefficient: 1.
- Multiply 1 by the root (4): [tex]\( 1 \times 4 = 4 \)[/tex].
- Add the result to the second coefficient (6): [tex]\( 4 + 6 = 10 \)[/tex].
- Now multiply 10 by the root (4): [tex]\( 10 \times 4 = 40 \)[/tex].
- Add this result to the last coefficient (-1): [tex]\( 40 + (-1) = 39 \)[/tex].
5. Conclusion: The remainder is the final number obtained after all the additions, which is 39.
So, the remainder when dividing the polynomial by [tex]\( x - 4 \)[/tex] is 39.
1. Identify the root: Since the divisor is given as [tex]\( x - 4 \)[/tex], the root is 4.
2. Write down the coefficients: For the polynomial described, the coefficients are 1, 6, and -1.
3. Begin synthetic division:
- Start with the first coefficient, which is 1.
- Multiply this number by the root (4) and add the result to the next coefficient.
4. Perform the calculations step-by-step:
- Start with the first coefficient: 1.
- Multiply 1 by the root (4): [tex]\( 1 \times 4 = 4 \)[/tex].
- Add the result to the second coefficient (6): [tex]\( 4 + 6 = 10 \)[/tex].
- Now multiply 10 by the root (4): [tex]\( 10 \times 4 = 40 \)[/tex].
- Add this result to the last coefficient (-1): [tex]\( 40 + (-1) = 39 \)[/tex].
5. Conclusion: The remainder is the final number obtained after all the additions, which is 39.
So, the remainder when dividing the polynomial by [tex]\( x - 4 \)[/tex] is 39.
