## bry856 one year ago what the heck is that formula

1. bry856

2. anonymous

3. bry856

how to i rewrite a rational expression into a quadratic one then?

4. Elsa213

GO NNESHA GO! :D

5. Nnesha

long division or synthetic division which one is easy for you ?

6. bry856

long division is easier

7. Nnesha

$\huge\rm qoutient + \frac{ remainder }{ divisor }$ quotient = q(x) remainder = r(x) divisor = b(x)

8. Nnesha

are you sure? leading coefficient of divisor is one so you do synthetic division which is really easy

9. bry856

x^2 -4x+1 is the solution the the equation in the photo, right?

10. bry856

oh okay i will do that then

11. bry856

thank you so much ive been trying to figure out what q(x), r(x), and b(x) stood for forever

12. Nnesha

alright for synthetic division x-3=0 solve for x x=3 write JUST coefficient |dw:1433942314956:dw| carry down first number and then multiply by 3

13. Nnesha

|dw:1433942396062:dw| multiply and then combine like terms -7 +1 = -6 multiply again

14. Nnesha

now try it ^^^

15. anonymous

The upper one is a cubic equation, but worry not and be smart about it. Notice that you have to divide the whole thing to (x-3) so there's a good chance 3 is a root for that cubic equation. Checks out it is. Divide the cubic one to (x-3) and you'll get your answer. Alternatively, you can be smart about that too and notice that (x^2-4x+1) is the only thing that makes sense since it's the only quadratic form (which you'd expect to have if you divide a cubic equation to a linear one) that "allows" for that -3 at the cubic equation to be formed. The other quadratic (the one with +13) when multiplied with (x-3) will give you something with -39 at the end so that's no good.

16. anonymous

So you can conclude that it divides evenly and that your answer is q=(x^2-4x+1) r=0 b=*could be just about anything but for the sake of math* x-3