Use synthetic division and the given factor to comletely factor each polynomial function y=x^3-3x^2-10x+24; (x-2). I divided it and got 1x^2+1x-12,Remainder 48.. Is this right and how do i factor it with the remainder?

Question

lgbasallote · Answer

what did you divide it with again?

anonymous · Answer

so i divided (x^3-3x^2-10x+24) by (x-2)

lgbasallote · Answer

i think you went wrong...there shouldn't be a remainder

anonymous · Answer

Hmmmmm I thought so ... let me try again

lgbasallote · Answer

i have to go now so good luck

anonymous · Answer

Thanks anyway!

jim_thompson5910 · Answer

Use synthetic division to get what you see attached

jim_thompson5910 · Answer

The first three numbers at the bottom represent the coefficients of the quotient, so the quotient is x^2 - x - 12

The last number is the remainder, which is 0. So 

(x^3-3x^2-10x+24)/(x-2) =  x^2 - x - 12

and you can rewrite the equation to get

x^3-3x^2-10x+24 =  (x-2) (x^2 - x - 12)

anonymous · Answer

I was doing that but i see i got my positive and negative signs tumbled up. Now i would just factor 1x^2-1x-12?

jim_thompson5910 · Answer

yes exactly

jim_thompson5910 · Answer

what do you get when you factor that

anonymous · Answer

okay hold on just a moment let me try and do this (:

jim_thompson5910 · Answer

alright

anonymous · Answer

would it be (x+3)(x-4)?

jim_thompson5910 · Answer

yes it is, 

(x+3)(x-4)

x(x-4) + 3(x-4)

x^2 - 4x + 3x - 12

x^2 - x - 12

So follow this backwards to factor x^2 - x - 12 into (x+3)(x-4)

jim_thompson5910 · Answer

So 

x^3-3x^2-10x+24

completely factors to

(x-2)(x+3)(x-4)

anonymous · Answer

Awesome!!! Okay i did that right! Thank you so much for your help (: (:

jim_thompson5910 · Answer

you're welcome

anonymous · Answer

:) :)