Answer:
No, (x-4) is not a factor of f(x) = x³ - 2x² + 5x + 1.
Explanation:
To determine whether (x-4) is a factor of a polynomial, we can try to divide the polynomial by (x-4) using polynomial long division. If the division is successful and the remainder is zero, then (x-4) is a factor of the polynomial.
If we divide f(x) by (x-4) using polynomial long division, we get:
x³ - 2x² + 5x + 1
(x-4)
x² - 4x
x² + x
x + 4
-----
x + 3
Since the remainder is not zero, (x-4) is not a factor of f(x).