Synthetic division of p(x)= 2x raised to the power of 4 - x raised to the power of 3 + 9x raised to the power of 2

p(x) = 2x^4 - x^3 + 9x^2
1. Convert to standard polynomial form:
2x^4 - x^3 + 9x^2 + 0x + 0
2. Coefficients:
[2, -1, 9, 0, 0]
3. Using synthetic division with the divisor (x - c):
Assuming c = 1,
- Write the coefficients:
2, -1, 9, 0, 0
- Synthetic division process:
- Bring down the leading coefficient (2).
- Multiply 2 by 1 and add to the next coefficient (-1):
2 + (-1) = 1
- Multiply 1 by 1 and add to 9:
1 + 9 = 10
- Multiply 10 by 1 and add to 0:
10 + 0 = 10
- Multiply 10 by 1 and add to 0:
10 + 0 = 10

4. The quotients give us the coefficients of the polynomial:
2, 1, 10, 10

5. Thus, the result of the synthetic division is:
2x^3 - 1x^2 + 10x + 10

Answer: 2x^3 - 1x^2 + 10x + 10