Use synthetic division to divide
9x^2-3x+8+5x^3/x+1
To divide the polynomial (5x^3 + 9x^2 - 3x + 8) by (x + 1) using synthetic division, follow these steps:
1. Write the coefficients of the polynomial in descending order:
5x^3 + 9x^2 - 3x + 8
2. Identify the divisor (x + 1) and set it equal to zero to find the divisor's value: x + 1 = 0 --> x = -1
3. Set up the synthetic division table by writing the divisor and the coefficients of the polynomial:
-1 | 5 9 -3 8
4. Bring the first coefficient (5) down directly below the division bar:
-1 | 5 9 -3 8
|
5. Multiply the divisor (-1) by the first term (5) and write the result below the next coefficient (9):
-1 | 5 9 -3 8
|-5
6. Add the corresponding terms in the second row and write the sum below the line:
-1 | 5 9 -3 8
|-5 -4
7. Repeat steps 5 and 6, continuing to bring down the next coefficient:
-1 | 5 9 -3 8
|-5 -4 7
8. The numbers in the bottom row represent the coefficients of the quotient and the remainder. Therefore, the quotient is 5x^2 - 4x + 7 and the remainder is 7.
Therefore, (5x^3 + 9x^2 - 3x + 8) / (x + 1) = 5x^2 - 4x + 7 with a remainder of 7.