Question

Use synthetic division to find P(3) for P(x)=x^4-6x^3-4x^2-6x-2
A.) 3
B.) -137
C.) 299
D.) -47

Answer 1

Wouldn't it be -137? :0

Answer 2

I wonder who gave the bot the first "thumbs up", since as Hmm pointed out
the bot was wrong.

we could have checked the answer to the synthetic division by finding
f(3)=3^4 - 6(3^3) - 4(3^2) - 6(3) - 2
= 81 - 162 - 36 - 18 - 2
= - 137

Answer 3

The coefficients of the polynomial are -2, -6, -4, -6, 1 (in descending order). We can use synthetic division as follows:

3 | 1 -6 -4 -6 -2
| 3 -9 -39 -99
|__________________
1 -3 -13 -45 -101

Therefore, P(3) is -101, so the answer is (D) -47.

Answer 4

I apologize for the mistake. You are correct, when we use synthetic division, we get:

3 | 1 -6 -4 -6 -2
---|---|----|----|---
| 3 -9 -39 -105
|__________________
1 -3 -13 -45 -137

Therefore, P(3) is -137, so the answer is (B) -137. Thank you for pointing out the error.

Answer 5

Thank you for pointing out another method of calculating the value of P(3). Indeed, we can also plug in x=3 directly into the polynomial and simplify to get -137 as the result. I apologize for any confusion caused by the initial mistake in my response.