Use synthetic division and the Remainder Theorem to find the indicated function value.
f(x) = x5 - 8x4 - 9x3 - 6; f(3)
I keep coming up with the answer of -222, but that is not an option... I don't know what I'm doing wrong!!! PLEASE HELP--I only have 20 mins left to submit this...
Thanks
I don't understand why you have to use synthetic division and the remainder theorem to compute the value of the function at x=3.
The answer is 2^5 -8*16 -9*8 -6 =-174
To use synthetic division and the Remainder Theorem to find the indicated function value, we need to divide the polynomial f(x) by x - c, where c is the constant in the function we are evaluating at. In this case, we are evaluating f(x) at x = 3, so c = 3.
Now let's go through the steps:
1. Write the coefficients of the polynomials in descending order of powers of x. In this case, f(x) = x^5 - 8x^4 - 9x^3 - 6 can be written as 1x^5 - 8x^4 - 9x^3 + 0x^2 + 0x - 6.
2. Set up the synthetic division table. Put the value of c, which is 3, on the left side of the table, and write down the coefficients of the polynomial to be divided on the top row.
```
3 | 1 -8 -9 0 0 -6
```
3. Bring down the first coefficient, which is 1, and write it under the horizontal line.
```
3 | 1 -8 -9 0 0 -6
1
```
4. Multiply the divisor, 3, by the number just brought down, 1. Write the product, 3, below the next coefficient of the polynomial being divided.
```
3 | 1 -8 -9 0 0 -6
1
---
3
```
5. Add the numbers in the second column and write the sum below the horizontal line.
```
3 | 1 -8 -9 0 0 -6
1
---
3
```
6. Repeat steps 4 and 5 until you reach the last coefficient.
```
3 | 1 -8 -9 0 0 -6
1 -3 -18 -54 -162 -486
---
3 -11 -27 -54 -162 -492
```
7. The last number on the bottom row is the remainder. In this case, the remainder is -492.
Therefore, the value of f(3) is -492.
It looks like you made a mistake when performing the synthetic division. Be careful with your calculations, and make sure to add and subtract the numbers correctly.