any idea how to get the zeros for x^3-4x^2+x+6 without using a graphing calculator? (can't figure out how to factor it out)

Question

any idea how to get the zeros for x^3-4x^2+x+6 without using a graphing calculator?  (can't figure out how to factor it out)

anonymous · Answer

I should say algebraically, I know I can make a table and just get lucky

dumbcow · Answer

try to factor out (x+-1), (x+-2)...up to 6
if that works you'll be left with a quadratic

dumbcow · Answer

actually you can factor out (x+1)
there are different ways of doing this
(x+1)(x^2 +bx +6) = x^3-4x^2+x+6
we have to find b, if b is an integer it works
x^2+bx^2 = -4x^2
(b+1)x^2 = -4x^2
b+1 = -4
b = -5

anonymous · Answer

ah long division, its been a while

dumbcow · Answer

long division always works too :)

anonymous · Answer

thanks

anonymous · Answer

You could also use the rational root theorem to discover the possible rational roots.