Can you use the remainder theorem when f(x) is divided by x-(1/3)?

timer Asked: Oct 30th, 2015
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Question Description

Use the remainder theorem to find the remainder when f(x) is divided by x-(1/3). Then use the factor theorem to determine whether x-(1/3) is a factor of f(x).

f(x)= 3x^4-x^3+15x-5

Then is x-(1/3) a factor of f(x)?

Really appreciate your help!! Thank you!

Tutor Answer

School: University of Virginia

Thank you for the opportunity to help you with your question!


The remainder theorem states that the remainder of the division of a polynomial f(x) by a linear polynomial x-a is equal to f(a) .

To find the remainder when f(x) is divided by x-(1/3) using remainder theorem, 

substitute x = 1/3 in f(x).

So the remainder is 0.

The factor theorem states that a polynomial f(x) has a factor (x - k) if and only if f(k)=0.

We showed that .

Hence, by factor theorem  is a factor of f(x).


Please let me know if you need any clarification. I'm always happy to answer your questions.

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