Find the value of `a ,` if `x-1` is a factor of `x^3-a^2x+x+2.`

Explanation

Let `P(x)=x^3-a^2x+x+2`
`if (x-1)` is a factor of `P(x)`,
`x-1=0`
`x=1`
Putting `x=1` in `P(x)`,
`1^3-a^2xx1+1+2=0`
`1-a^2+3=0`
`-a^2+4=0`
`a^2=4`
`a=2`
Hence, the value of `a` is `2`.