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

shyamnair3
School: University of Virginia   -------------------------------------------------------------------------------

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

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

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

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 $f(k)=0$.

Hence, by factor theorem $f(k)=0$ is a factor of f(x).

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