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Answer :
To solve this synthetic division problem, let's find the remainder when we divide the polynomial by [tex]\( x - 3 \)[/tex].
The polynomial given by the coefficients is [tex]\( 1x^2 + 2x - 3 \)[/tex].
When performing synthetic division:
1. List the coefficients of the polynomial: [tex]\( [1, 2, -3] \)[/tex].
2. Since the divisor is [tex]\( x - 3 \)[/tex], we use the root [tex]\( x = 3 \)[/tex].
Begin the synthetic division:
- Bring down the first coefficient: [tex]\( 1 \)[/tex].
Now, perform the synthetic division process:
1. Multiply the root (3) by the result so far (1), and then add the next coefficient (2):
- [tex]\( 1 \cdot 3 = 3 \)[/tex]
- [tex]\( 3 + 2 = 5 \)[/tex]
2. Multiply the root (3) by the new result (5), and then add the next coefficient (-3):
- [tex]\( 5 \cdot 3 = 15 \)[/tex]
- [tex]\( 15 + (-3) = 12 \)[/tex]
The last number you reach is the remainder, which is 12.
Therefore, the remainder of the division is 12. However, this result is not listed in the multiple-choice options. It appears there might be an oversight or a typo in the options provided. Double-check your input or the context of the question to ensure all details are accurately represented.
The polynomial given by the coefficients is [tex]\( 1x^2 + 2x - 3 \)[/tex].
When performing synthetic division:
1. List the coefficients of the polynomial: [tex]\( [1, 2, -3] \)[/tex].
2. Since the divisor is [tex]\( x - 3 \)[/tex], we use the root [tex]\( x = 3 \)[/tex].
Begin the synthetic division:
- Bring down the first coefficient: [tex]\( 1 \)[/tex].
Now, perform the synthetic division process:
1. Multiply the root (3) by the result so far (1), and then add the next coefficient (2):
- [tex]\( 1 \cdot 3 = 3 \)[/tex]
- [tex]\( 3 + 2 = 5 \)[/tex]
2. Multiply the root (3) by the new result (5), and then add the next coefficient (-3):
- [tex]\( 5 \cdot 3 = 15 \)[/tex]
- [tex]\( 15 + (-3) = 12 \)[/tex]
The last number you reach is the remainder, which is 12.
Therefore, the remainder of the division is 12. However, this result is not listed in the multiple-choice options. It appears there might be an oversight or a typo in the options provided. Double-check your input or the context of the question to ensure all details are accurately represented.
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