Is x-3 a factor of $x^3-6x^2-x+30$ ?

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Answer 1 · 2016-08-26T15:11:37

If $a$ is a root of a polynomial $P(x)$ (that is $P(a)=0$ ), then $P(x)$ is divisible by $(x-a)$

So, we need to evaluate $P(3)$ . That is:

$3^3-(6*3^2)-3+30=27-54-3+30=27-57+30=0$

and so the polynomial give is divisible by $(x-3)$

Is x-3 a factor of x^3-6x^2-x+30x^3-6x^2-x+30?