Is (x-4) a factor of f(x)=x^3-2x^2+5x+1 ? use either the remainder theorem or the factor theorem to explain your reasoning

No, (x-4) is not a factor of f(x).

Step-by-step explanation:

Remainder Theorem:

When a Polynomial f(x) is divided by (x-a),then the remainder will be f(a).

Therefore from Remainder theorem,

We can say that '(x-a) is a factor of f(x) if f(a)=0' (since f(a) is the remainder, it should be equal to 0 for (x-a) to be a factor of f(x))

So now we divide our f(x) with (x-4) and check the remainder f(4).

Given,

f(x) =

So when f(x) is divided by (x-4) remainder will be f(4)

remainder = f(4) = = 53.

Therefore since remainder is not equal to 0,when f(x) is divided by (x-4)

We can say that,

(x-4) is not a factor of f(x)

step-by-step explanation:

most likely the answer is a.

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the diameter is 16 cm. are you a teacher?

step-by-step explanation: