what the heck is that formula

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what the heck is that formula

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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

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GO NNESHA GO! :D
long division or synthetic division which one is easy for you ?
long division is easier
\[\huge\rm qoutient + \frac{ remainder }{ divisor }\] quotient = q(x) remainder = r(x) divisor = b(x)
are you sure? leading coefficient of divisor is one so you do synthetic division which is really easy
x^2 -4x+1 is the solution the the equation in the photo, right?
oh okay i will do that then
thank you so much ive been trying to figure out what q(x), r(x), and b(x) stood for forever
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
|dw:1433942396062:dw| multiply and then combine like terms -7 +1 = -6 multiply again
now try it ^^^
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.
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

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