Question

Is (x+2) a factor of f(x)=x^3+x^2-16x-16. use synthetic division and factor theorem

Answer 1

No its not :)

Explanation:

To check whether \( (x+2) \) is a factor of \( f(x) = x^3 + x^2 - 16x - 16 \), we can use synthetic division.

The synthetic division process involves dividing \( f(x) \) by \( (x+2) \). If the result is zero, then \( (x+2) \) is a factor.

Here's the synthetic division:

```

-2 | 1 1 -16 -16

| -2 -6 44

__________________

1 -1 -22 28

```

The result is \( x^2 - x - 22 \), with a remainder of 28.

Since the remainder is not zero, \( (x+2) \) is not a factor of \( f(x) \).