Divide using synthetic division.
-3x^3 + 11x^2 - x + 20 by (x - 4)
it is easy to tell that you are wrong, since the division produces f(4), which in no way can be -152.
In fact, (-3x^3 + 11x^2 - x + 20) / (x - 4) = -3x^2-x-5
with a remainder of 0.
Where did you get that -44?
4 | -3 11 -1 20
...|... -12 -4 -20
-------------------------
...| -3 -1 -5 0
To use synthetic division, we need to set up the problem using the coefficients of the terms in descending order:
Dividend: -3x^3 + 11x^2 - x + 20
Divisor: x - 4
First, we write down the coefficients of the terms of the dividend (including zero coefficients):
-3 11 -1 20
Next, write down the root of the divisor, changing the sign:
4
Now, perform the synthetic division. Bring down the first coefficient, multiply it by the root, and write the result under the next coefficient. Add the two values together and continue the process:
4 | -3 11 -1 20
| -12 -44 -172
-------------------------
| -3 -1 -13 -152
The final line represents the quotient of the division. Thus, the result of dividing -3x^3 + 11x^2 - x + 20 by (x - 4) is -3x^2 - x - 13, with a remainder of -152.
You are right, I apologize for the mistake in my previous response. The correct synthetic division is as follows:
4 | -3 11 -1 20
| 4 60 236
----------------------
-3 15 59 256
So, the result of dividing -3x^3 + 11x^2 - x + 20 by (x - 4) is -3x^2 + 15x + 59, with a remainder of 256.