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Answer :
Sure! Let's go through synthetic division step-by-step to find the remainder when dividing the polynomial by [tex]\( x - 1 \)[/tex].
The polynomial we have is represented by the coefficients: [tex]\( 4, 6, -3 \)[/tex]. This represents the polynomial [tex]\( 4x^2 + 6x - 3 \)[/tex].
The divisor is [tex]\( x - 1 \)[/tex], which means we use [tex]\( 1 \)[/tex] in synthetic division.
Here's a step-by-step breakdown of the process:
1. Write the coefficients: Start with the coefficients of the polynomial: [tex]\( 4, 6, -3 \)[/tex].
2. Bring down the leading coefficient: Begin by writing the first coefficient, which is 4, as the first number in the bottom row.
3. Multiply and add: Multiply this number (4) by the divisor (1), and place the result under the next coefficient (6). So, [tex]\( 4 \times 1 = 4 \)[/tex].
4. Add the result to the next coefficient: Add this result to the next coefficient: [tex]\( 6 + 4 = 10 \)[/tex]. Write 10 in the bottom row below the 6.
5. Repeat the multiply and add process: Multiply 10 by 1, and write the result under the next coefficient (-3). So, [tex]\( 10 \times 1 = 10 \)[/tex].
6. Add the result to the last coefficient: Add this result to the last coefficient: [tex]\( -3 + 10 = 7 \)[/tex].
The final number, written in the bottom row, is the remainder.
Therefore, the remainder when dividing by [tex]\( x - 1 \)[/tex] is [tex]\( 7 \)[/tex].
The correct answer is D. 7.
The polynomial we have is represented by the coefficients: [tex]\( 4, 6, -3 \)[/tex]. This represents the polynomial [tex]\( 4x^2 + 6x - 3 \)[/tex].
The divisor is [tex]\( x - 1 \)[/tex], which means we use [tex]\( 1 \)[/tex] in synthetic division.
Here's a step-by-step breakdown of the process:
1. Write the coefficients: Start with the coefficients of the polynomial: [tex]\( 4, 6, -3 \)[/tex].
2. Bring down the leading coefficient: Begin by writing the first coefficient, which is 4, as the first number in the bottom row.
3. Multiply and add: Multiply this number (4) by the divisor (1), and place the result under the next coefficient (6). So, [tex]\( 4 \times 1 = 4 \)[/tex].
4. Add the result to the next coefficient: Add this result to the next coefficient: [tex]\( 6 + 4 = 10 \)[/tex]. Write 10 in the bottom row below the 6.
5. Repeat the multiply and add process: Multiply 10 by 1, and write the result under the next coefficient (-3). So, [tex]\( 10 \times 1 = 10 \)[/tex].
6. Add the result to the last coefficient: Add this result to the last coefficient: [tex]\( -3 + 10 = 7 \)[/tex].
The final number, written in the bottom row, is the remainder.
Therefore, the remainder when dividing by [tex]\( x - 1 \)[/tex] is [tex]\( 7 \)[/tex].
The correct answer is D. 7.
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