Question

Use the factor theorem to determine if (x-4) . is a factor of x^5 - 3x^4 - x - 3

Answer 1

(x - 4) is not a factor because
`f(4) \\eq 0`.

Explanation:

According to the factor theorem, if f(x) = 0, only then f(x) can have a factor (x-a) which in this case is equal to (x - 4).

Considering this factor theorem, we can write it as:

`f(x) = x^(5) - 3x^(4) - x - 3`

Now to check if (x - 4) is its factor or not, substitute a value of 4 in place of x in f(x):

`f(4) = (4)^(5) - 3(4)^(4) - (4) - 3`
`= 249`

So f(x) is not equal to zero which means (x - 4) is not a factor of
`x^(5) - 3x^(4) - x - 3`