Question

Use the Remainder Theorem to completely factor p(x) = x^3 - 6x^2 + 11x - 6

Please show your work

Answer 1

By the rational root theorem, we have several possible candidates for roots:
`\pm1,\pm2,\pm3,\pm6`

Plugging each of these options in, you find that
`p(x)=0` for
`x=1,2,3`. The polynomial remainder theorem states that
`x-c` is a factor of
`p(x)` if and only if
`p(c)=0`.

This means


`p(x)=(x-1)(x-2)(x-3)`