g(x)=X^2-12x^2+46x-52 has real root x=2 . FInd the remaining roots and factor g completley.

Question

whpalmer4 · Answer

Are you sure you've typed that correctly?

anonymous · Answer

oh your right thats supposed to be a x^3

whpalmer4 · Answer

Well, one obstacle out of the way :-)

How will you proceed?

anonymous · Answer

yeah :] well i did synthetic division

anonymous · Answer

and found if it had a zero but i dont know how to factor g

whpalmer4 · Answer

Well, what do you have left after you divide out (x-2)?

anonymous · Answer

theres a 1 -10 26

whpalmer4 · Answer

So as a polynomial, that would be...

anonymous · Answer

um x^3-10x^2 +26?

whpalmer4 · Answer

no...we had an x^3 and divided by x, so that represents...

anonymous · Answer

x^2?

anonymous · Answer

i feel like i did sometihing wrong on the equation

whpalmer4 · Answer

After we divide out (x-2) we are left with x^2-10x+26, which cannot be factored, but can be solved by the quadratic equation, or completing the square.  What do you get for the roots when you do so?