Find all the zeroes of polynomial $x^{3} - 8 x^{2} + 5 x + 50$ .

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Solution

Since, it is a cubic polynomial we can try hit and trial method.
So, try with -1,1,2,-2
So, when we substitute x = -2, the expression will become zero.
Now, (x+2) is the first zero.
Then by long division method find the quotient, it is $(x^{2} - 10 x + 25)$
So, factor of $x^{3} - 8 x^{2} + 5 x + 50 = (x + 2) (x^{2} - 10 x + 25)$
$= (x + 2) (x - 5) (x - 5)$

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