Is x-5 a factor of $x^{3} + 6 x^{2} - 7 x - 60$ $x^3+6x^2-7x-60$ ?

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Answer 1 · 2016-08-22T18:08:57

No

The factor theorem states that if , for a given function f(x) , f(a)=0 then x-a is a factor of f(x)

Think about the function (x-5)( $x^{2} + 3 x - 5)$ $x^2+3x-5)$
Clearly x-5 is a factor and if you substitute 5 into the function the result will be 0

fx= $x^{3} + 6 x^{2} - 7 x - 60$ $x^3+6x^2-7x-60$
f(5)=125+150-35-60 this is not zero so x-5 is not a factor

Is x-5 a factor of x3+6x2−7x−60x^3+6x^2-7x-60?