Given 2x^3-15x^2+27x-10=0, where x=1/2, use synthetic division to show that x is a solution of the third-degree polynomial equation and use the result to factor the polynomial completely. List all real solutions.

Question

MiraAngel · Answer

There are no diagrams to upload for this problem. I got a messages on here to make sure I upload any. Just wanted to let anyone who comes this post that there's no diagram to go with it

MiraAngel · Answer

@Isolation

Isolation · Answer

I'm confused... it gives you the x-value.... but what's you to use synthetic division? to divide what?
or does it mean to divide all that with (x-1/2)

Isolation · Answer

If that's the case... I'd prefer to use long division... lol

Isolation · Answer

But you still can use long division... but 1/2 as that little number thing

what'd you get if you do it

jhonyy9 · Answer

so given x =  1/2 or 2x = 1 from what result that you can divide this equation by (x - 1/2)  or (2x - 1)

surjithayer · Answer

do you know the process of synthetic division?
write  coefficients of  the given eq. and  then start.
1/2|2  -15    27  -10     write 2,then multiply by 1/2,you get  1 ,write and add you get -14 
      |       1     -7   10     again multiply by 1/2,you get -7,write and add ,you get 20 ,
     _________________    again multiply by 1/2,you get 10 ,again multiply by 1/2 ,you get 10,
          2  -14  20  | 0    add ,remainder =0
now you get aquadratic eq.
can you write it?

surjithayer · Answer

i have written twice agai multiply by 1/2,you get 10 by mistake

surjithayer · Answer

it is only once.

surjithayer · Answer

can you make factors of this quadratic?

MiraAngel · Answer

O_O that's a lot to take in lol