Question

Use the Rational Root Theorem to list all possible rational roots for each
equation. Then find any actual rational roots.

x^3 - 4x^2 - 15x + 18

Answer 1

all possible rational roots is a lot. numerator has to divide 18, denominator has to divide the leading coefficient, which is 1
so they are
\[\pm1,\pm2,\pm 3,\pm 6, \pm9,\pm18\]

Answer 2

actual ones are -3, 1, 6 because this is
\[(x+3)(x-1)(x-6)\]

Answer 3

a good question is "how did you know this factors?"and the answer is i tried 1, which obviously works, because
\[1-4-15+18=0\]then you can factor out
\[(x-1)\]and see what you get

Answer 4

why factor out 1?

Answer 5

because i know that 1 is a root, so it has to factor out

Answer 6

how would you factor it out?