If x= 3/7 is a root of 49x^3 - 189x^2+135x -27 = 0, use synthetic division to factor the polynomial completely and list all real solutions of the equations.

Question

moonlitfate · Answer

I know that since x = 3/7, that means that (7x-3) is a factor.

amorfide · Answer

okay so write down

(7x-3)  


okay so

7x times what gives 49x^3?

moonlitfate · Answer

7x^2

amorfide · Answer

so the fist value in your second bracket is 7x^2

(7x-3)(7x²

now multiply 7x² by -3

then how many more do you need to get 189x²?

amorfide · Answer

-189x² i meant

moonlitfate · Answer

Oh, so just use long division.  Working out the answer to that part right now.

anonymous · Answer

|dw:1349977323030:dw|

moonlitfate · Answer

I got 7x^2-24x+9

amorfide · Answer

you are right

amorfide · Answer

you might be able to factorise the quadratic you have

moonlitfate · Answer

Factored 7x^2-24x + 9 into:  (7x-3) (x-3); so the factors are: (7x-3)^2 (x-3).  So the roots are x= 3/7 and x=3. :)

amorfide · Answer

well done!

amorfide · Answer

x does not = 7 how did you get that guy?

anonymous · Answer

Oops, You're correct! 
 21/7 = 3

moonlitfate · Answer

Thanks for the help @amorfide :)

amorfide · Answer

anytime! just happy to help