Answer
$x-1$ is a factor
Work Step by Step
The picture below shows the result of $(
3x^3+10x^2-x-12
)\div(
x-1
)$ using synthetic division.
The numbers in the last row in the picture below are the coefficients of the quotient and the remainder.
In that row, the left-most number is the coefficient of $
x^3
$ (leading term of dividend) divided by $
x
$ (leading term of divisor).
Since $
x^3\div x=x^2
,$ then the left-most number is the coefficient of $
x^2
$ and the next numbers are the coefficients of $x$ in decreasing exponent (down to exponent $0$).
The right-most number, on the other hand, represents the remainder.
Since the remainder is $0,$ then $
x-1
$ is a factor of $
3x^3+10x^2-12
.$