Answer :
Sure, let's go through the synthetic division step-by-step:
We have the polynomial [tex]\( P(x) = 2x^3 - 4x^2 - 9x + 1 \)[/tex] and we are dividing it by [tex]\( x - 2 \)[/tex]. The divisor, [tex]\( x - 2 \)[/tex], means we'll use the value 2 for our synthetic division.
1. Set up the coefficients: The coefficients of the polynomial are 2, -4, -9, and 1.
2. Carry down the leading coefficient: We start by bringing down the first coefficient, which is 2.
3. Multiply and add:
- Multiply the number brought down (2) by the divisor (2), which gives 4.
- Add this result (4) to the next coefficient (-4). The sum is 0.
4. Repeat the process:
- Multiply the result (0) by the divisor (2), resulting in 0.
- Add it to the next coefficient (-9). The sum is -9.
- Multiply -9 by the divisor (2), resulting in -18.
- Add this to the last coefficient (1), giving a final sum of -17.
The remainder of this synthetic division is -17.
So, the correct answer is A. -17.
We have the polynomial [tex]\( P(x) = 2x^3 - 4x^2 - 9x + 1 \)[/tex] and we are dividing it by [tex]\( x - 2 \)[/tex]. The divisor, [tex]\( x - 2 \)[/tex], means we'll use the value 2 for our synthetic division.
1. Set up the coefficients: The coefficients of the polynomial are 2, -4, -9, and 1.
2. Carry down the leading coefficient: We start by bringing down the first coefficient, which is 2.
3. Multiply and add:
- Multiply the number brought down (2) by the divisor (2), which gives 4.
- Add this result (4) to the next coefficient (-4). The sum is 0.
4. Repeat the process:
- Multiply the result (0) by the divisor (2), resulting in 0.
- Add it to the next coefficient (-9). The sum is -9.
- Multiply -9 by the divisor (2), resulting in -18.
- Add this to the last coefficient (1), giving a final sum of -17.
The remainder of this synthetic division is -17.
So, the correct answer is A. -17.
