Question

Find the zeros of x³-6x²+11x-6

Answer 1

ANSWER

3, 2, 1

How to solve : Use factor theorem

I'll let $f_{(x)}=x^3-6x^2+11x-6$

Then $f_{(1)}=0$

According the factor theorem, it has factor $x-1$

To continue, we must divide $f_{(x)}$ by $x-1$

The division ends without remainder.

Quotient : $x^2-5x+6$

The quotient is factored into $(x-3)(x-2)$

So $f_{(x)}=(x-3)(x-2)(x-1)$

Hence the zeros are $x=3,2,1$.