Question

How do you find all the zeros of `x^3-3x^2-x+3` with 3 as a zero?

Answer 1

The zeros are `x=3` and `x=-1` and `x=+1`

Explanation:

By synthetic division, arrange the numerical coefficients according to degree(from highest to lowest)

`x^3" " " " " "x^2" " " " " "x^1" " " " " "x^0`

`1" " " "-3" " " "-1" " " " " " "3" " " " " "|__underline( 3 )`
`underline(" " " " " " " 3" " " " " " " 0" " " " "" " -3`
`1" " " " " "0" " " " " -1" " " " " " " 0" " "larr`the remainder

Our depressed equation is now

`x^2+0*x-1=0`

which is reduced by 1 degree from degree 3.
Solve for the remaining roots

`x^2-1=0`

`x^2=1`

`sqrt(x^2)=+-sqrt(1)`

`x=-1` and `x=+1`

God bless...I hope the explanation is useful