How do you use the factor theorem to determine whether x-1 is a factor of $f (x) = x^{3} + 4 x - 5$ $f(x)=x^3+4x-5$ ?

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Answer 1 · 2016-01-06T17:27:27

Calculate $f (1)$ $f(1)$ .

If $f (1) = 0$ $f(1) = 0$ , then $x - 1$ $x - 1$ is a factor of $f$ $f$ . So let's calculate $f (1)$ $f(1)$ .

$f (1) = 1 + 4 - 5 = 5 - 5 = 0$ $f(1) = 1 + 4 - 5 = 5 - 5 = 0$ . So $1$ $1$ is a root of this polynomial, and $x - 1$ $x - 1$ is a factor of it.

How do you use the factor theorem to determine whether x-1 is a factor of f(x)=x^3+4x-5f(x)=x3+4x−5f(x)=x^3+4x-5?