Need some help with using synthetic division to find the function value of this problem:
f(x)=2x^4+4x^3+2x^2+3x+8;find f(-2)
hard to line up the spacing with this font format, but here it goes
-2│2 4 2 3 8
***----------
*** -4 0-4 2
** 2 0 0-1 10
so f(-2) = 10
the last row in the synthetic division algorithm should have been
** 2 0 2 -1 10
To find the value of the function f(x) when x = -2 using synthetic division, follow these steps:
Step 1: Write down the coefficients of the polynomial equation in descending order. In this case, the polynomial is f(x) = 2x^4 + 4x^3 + 2x^2 + 3x + 8, so the coefficients are 2, 4, 2, 3, and 8.
Step 2: Set up the synthetic division table. Since we are finding f(-2), we will write (-2) as the divisor in the first row of the table, and write the coefficients of the polynomial in the second row. Leave enough space for the additional rows that will be used in the synthetic division process.
| -2 | 2 | 4 | 2 | 3 | 8 |
Step 3: Begin the synthetic division process. Bring down the first coefficient, which is 2, to the bottom row.
| -2 | 2 | 4 | 2 | 3 | 8 |
2
Step 4: Multiply the divisor (-2) by the value at the bottom row. Write the result below the next coefficient (which is 4 in this case).
| -2 | 2 | 4 | 2 | 3 | 8 |
2
-4
Step 5: Add the value in the bottom row with the result obtained in the previous step. Write the sum below the next coefficient (which is 2 in this case).
| -2 | 2 | 4 | 2 | 3 | 8 |
2
-4
2
Step 6: Repeat steps 4 and 5 until all the coefficients have been used.
| -2 | 2 | 4 | 2 | 3 | 8 |
2
-4
2
-6
Step 7: The number in the bottom row is the last value obtained from the synthetic division process. This value represents the remainder of the division.
Step 8: Evaluate f(-2) by substituting x = -2 and using the remainder obtained in step 7. Since the remainder is -6, we have:
f(-2) = -6
Therefore, the value of the function f(x) when x = -2 is -6.