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

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Answer 1 · 2015-12-05T22:11:53

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

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

$f (5) = 2 \cdot 5^{3} + 5 \cdot 5^{2} - 14 \cdot 5 - 72$ $f(5)=2*5^3+5*5^2-14*5-72$

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

$f (5) = 375 - 142$ $f(5)=375-142$

$f (5) = 233$ $f(5)=233$

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

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)=2x3+5x2−14x−72f(x) = 2x^3 +5x^2 -14x -72?