The correct answer is:
2x² + 4x + 5
Step-by-step explanation:
We first write this in standard form:
2x³+0x²+-3x-10
To set up synthetic division, we use the coefficients from the polynomial at the top:
2 0 -3 -10
To the side, we will use 2 in the box:
2| 2 0 -3 -10
We drop the first coefficient, 2, down:
2| 2 0 -3 -10
2
Next we multiply by the 2 in the box. This gives us 4 to put under the 0. We then add 0+4, which gives us 4.
We then multiply this by 2. This gives us 8 to go under the -3. We then add -3+8, which gives us 5.
We then multiply this by 2. This gives us 10 to go under the -10; adding this gives us 0.
The bottom is then 2, 4, 5, 0. This means we have 2x²+4x+5 with a remainder of 0.