What is the quotient when x³ - 2x² - 5x + 6 is divided by x - 1?

Divide by $x-1$ using synthetic division with $1$: the coefficients $1,-2,-5,6$ give $1,\ -1,\ -6,\ 0$. The quotient is $x^2-x-6$ with remainder $0$, choice D. Check by multiplying: $(x-1)(x^2-x-6)=x^3-x^2-6x-x^2+x+6=x^3-2x^2-5x+6$. Choice B ($x^2+x-6$) has the wrong sign on the middle term. Choice A ($x^2-x+6$) has the wrong sign on the constant. Choice C ($x^2-3x-2$) comes from an arithmetic error in the bring-down steps. Multiplying back is the fastest way to verify.