Question

Divide: Left Parenthesis x-cubed minus 20 x plus 16 Right Parenthesis divided by Left Parenthesis x minus 4 Right Parenthesis
A. Negative x-squared plus 4 x plus 4
B. x-squared plus 4 x minus 4
C. Negative x-squared minus 4 x minus 4
D. x-squared minus 4 x plus 4

Answer 1

AAAaannndd the bot gets it wrong yet again!

Left Parenthesis x-cubed minus 20 x plus 16 Right Parenthesis divided by Left Parenthesis x minus 4 Right Parenthesis
(x^3-20x+16)/(x-4) = x^2+4x-4
So, B

Answer 2

The first step in synthetic division is to write down the coefficient of the divisor, which is just 1 since the divisor is x - 4. Then we write down the coefficients of the dividend in decreasing order of degree:

```
4 | 1 0 -20 16
```

The first number outside the division symbol is always the result of dividing the first coefficient of the dividend by the divisor (in this case, 1 divided by 4 is 1/4). We write that number below the line, and then multiply it by the divisor and write it under the next coefficient of the dividend:

```
1
4 | 1 0 -20 16
4 0 -80
```

We add the numbers in the second row to get:

```
1
4 | 1 0 -20 16
4 0 -80
---------
1 4 -20 -64
```

The result is a quotient of x^2 + 4x - 20 and a remainder of -64. Therefore, we can write:

```
x^3 - 20x + 16 = (x - 4)(x^2 + 4x - 20) - 64
```

Simplifying the quadratic factor gives us:

```
x^2 + 4x - 20 = (x + 2)(x - 10)
```

Putting everything together, we have:

```
x^3 - 20x + 16 = (x - 4)(x^2 + 4x - 20) - 64
= (x - 4)(x + 2)(x - 10) - 64
```

Therefore, the correct answer is C. Negative x-squared minus 4 x minus 4.

Answer 3

You are correct, I apologize for the mistake in my previous response. The correct answer is indeed B. x-squared plus 4 x minus 4. Thank you for bringing it to my attention.