How do you use the factor theorem to determine whether x+1/3 is a factor of $f (x) = 3 x^{4} + x^{3} - 3 x + 1$ $f(x) = 3x^4 + x^3 - 3x + 1$ ?

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How do you use the factor theorem to determine whether x+1/3 is a factor of $f (x) = 3 x^{4} + x^{3} - 3 x + 1$ $f(x) = 3x^4 + x^3 - 3x + 1$ ?

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Answer 1 · 2015-12-05T16:43:14

It is not a factor since $f (- \frac{1}{3}) \neq 0$ $f(-1/3)!=0$
So it will leave a remainder when long divided in.

Explanation:

If $(x + \frac{1}{3})$ $(x+1/3)$ is a factor of $f (x)$ $f(x)$ , then when divided into f it must leave no remainder, ie. $f (- \frac{1}{3})$ $f(-1/3)$ must be zero.

But : $f (- \frac{1}{3}) = 3 {(- \frac{1}{3})}^{4} + {(- \frac{1}{3})}^{3} - 3 (- \frac{1}{3}) + 1$ $f(-1/3)=3(-1/3)^4+(-1/3)^3-3(-1/3)+1$

$= 2$ $=2$

$\neq 0$ $!=0$

$therefore (x+1/3)$ is not a factor of $f(x)$ .

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How do you use the factor theorem to determine whether x+1/3 is a factor of $f (x) = 3 x^{4} + x^{3} - 3 x + 1$ $f(x) = 3x^4 + x^3 - 3x + 1$ ?

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Explanation:

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How do you use the factor theorem to determine whether x+1/3 is a factor of $f (x) = 3 x^{4} + x^{3} - 3 x + 1$ $f(x) = 3x^4 + x^3 - 3x + 1$ ?