How do you use the factor theorem to determine whether x-5 is a factor of $f(x) = 2x^3 +5x^2 -14x -72$ ?

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Answer 1 · 2015-12-05T22:11:53

$x-5$ is not a factor of $f(x)$

To see if $(x-5)$ is a factor of $f(x)$ we have to check if $f(5)=0$

$f(5)=2*5^3+5*5^2-14*5-72$

$f(5)=250+125-70-72$

$f(5)=375-142$

$f(5)=233$

$f(5)!=0$ so $(x-5)$ is not a factor of $f(x)$

How do you use the factor theorem to determine whether x-5 is a factor of f(x) = 2x^3 +5x^2 -14x -72f(x) = 2x^3 +5x^2 -14x -72?