x^3+3x^2-4 Find all rational zeros of the polynomial. (Enter your answers as a comma-separated list. If a zero has multiplicity greater than one, only enter the root once.)

Question

anonymous · Answer

Use synthetic division to test your possible roots.  This problem works out very quickly using that method.  The possible roots in this problem are all integers, so it is easy.

campbell_st · Answer

try x =1 and if f(1) = 0 then (x - 1) is a factor 


then do some polynomial division or synthetic divison to find the other factor(s)

campbell_st · Answer

you can also use the rational zeros test 

find the factors of the constant term -4 and let them p 

$$\pm 1, \pm2 \pm 4$$

find the factor of the leading term   1  and let them equal q   

$$\pm 1$$

then the rational zeros will be  $$\frac{p}{q} $$

so you can try f(-1), f(2), f(-2), f(4) and f(-4)

which ever result in a zero will be a factor

but this doesn't help with multiplicity.. 

as one of the  zeros has multiplicity of 2