Chapter R - Algebra Reference - R.1 Polynomials - R.1 Exercises - Page R-5: 22

$(x-1)(x+2)(x-3)=x^{3}-2x^{2}-5x+6$

$(x-1)(x+2)(x-3)$ First, evaluate $(x-1)(x+2)$ and simplify: $(x-1)(x+2)(x-3)=(x^{2}+2x-x-2)(x-3)=...$ $...=(x^{2}+x-2)(x-3)=...$ Now, evaluate $(x^{2}+x-2)(x-3)$ and simplify again: $...=x^{3}-3x^{2}+x^{2}-3x-2x+6=...$ $...=x^{3}-2x^{2}-5x+6$