Is (x − 4) a factor of f(x) = x3 − 2x2 + 5x + 1? use either the remainder theorem or the factor theorem to explain your reasoning.

ANSWER

Not a factor

EXPLANATION

The given polynomial function is:

According to the remainder theorem,if (x-4) is a factor of f(x), then f(4)=0.

We substitute x=4 into the function to obtain;

Since the remainder is not zero, x-4 is not a factor.

  No, (x - 4) is NOT a factor of the polynomial f(x).

Step-by-step explanation:  We are given to check whether (x − 4) a factor of the following polynomial :

We will be using factor theorem states as follows :

FACTOR THEOREM :  If (x - a) is a factor of the polynomial p(x), then p(a) = 0.

Now, substituting x = 4 in equation (i), we get

Since f(4) ≠ 0, so (x - 4) is NOT a factor of the polynomial f(x).

Thus, (x - 4) is not a factor of the polynomial f(x).

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