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
Wouldn't it be -137? :0
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.
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.
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
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.
To find P(3) using synthetic division, we need to perform synthetic division with the divisor of (x - 3) and the polynomial P(x) = x^4 - 6x^3 - 4x^2 - 6x - 2.
The synthetic division proceeds as follows:
3 | 1 -6 -4 -6 -2
| 3 -9 -39 -105
_____________________
1 -3 -13 -45 -107
After performing the synthetic division, we obtain the remainder as the last value in the bottom row, which is -107.
Therefore, P(3) = -107.
The correct answer is not listed among the options provided.