Find all values of m which will make x + 2 a factor of x^3 + 3m^2x^2 + mx + 4

Question

brinazarski · Answer

I got 2... is that correct? Are there others?

hartnn · Answer

if x+2 is the factor then x=-2 will satisfy the equation.
so did u put x=-2 and then got m=2 ??

brinazarski · Answer

No, I just used guess and check... tried (x+2)(x^2 +2), that didn't work, so I did (x+2)(x+1)(x+2) and that seemed to work...

hartnn · Answer

but i m getting -1/2 and 2/3

hartnn · Answer

(x+2)(x+1)(x+2) = x^3 +5x^2+8x+4

hartnn · Answer

u will get a quadratic in m when u put x=-2
solve that

brinazarski · Answer

-12m^2 + -2m - 4?

hartnn · Answer

nopes, somewhere u have done algebraic mistake, check it.

hartnn · Answer

its 12m^2 + -2m - 4=0

brinazarski · Answer

brb for a few minutes

shubhamsrg · Answer

did you try long division,?
after you do that, whatever is the remainder,put it to 0 and solve for m i guess..

brinazarski · Answer

Back, sorry, not supposed to be up at this hour lol

hartnn · Answer

still have doubts ? where ?

brinazarski · Answer

Like everywhere.... I just don't get it ._. How'd you get positive 12?

hartnn · Answer

+3m^2x^2 = +3m^2(-2)^2 = +3 m^2(4) =12m^2

brinazarski · Answer

Nvm I see that now x_x; Thank you

hartnn · Answer

did u get this ?
if x+2 is the factor then x=-2 will satisfy the equation.
or any more doubts ?

brinazarski · Answer

I think I got your answer.... so it's -1/2 and 2/3?

hartnn · Answer

yup.

brinazarski · Answer

Yes I got your answer :) Thank you!

hartnn · Answer

welcome :)