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anonymous
 one year ago
What is the quotient: (3x^3 + 14x^2 + 13x  6) / (3x  1) ?
anonymous
 one year ago
What is the quotient: (3x^3 + 14x^2 + 13x  6) / (3x  1) ?

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AbdullahM
 one year ago
Best ResponseYou've already chosen the best response.0Do you know group factoring?

AbdullahM
 one year ago
Best ResponseYou've already chosen the best response.0Group factoring is like: \[x^3 + x^2 + x + 1 = x^2(x+1) + 1(x+1) = (x+1)(x^2+1)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I don't really remember learning about that, but I think I understand a little bit

AbdullahM
 one year ago
Best ResponseYou've already chosen the best response.0so you need to group factor the numerator

AbdullahM
 one year ago
Best ResponseYou've already chosen the best response.0oh, wait. It can't be group factored >.<

AbdullahM
 one year ago
Best ResponseYou've already chosen the best response.0The Rational Root Theorem tells you that if the polynomial has a rational zero then it must be a fraction p/q, where p is a factor of the trailing constant and q is a factor of the leading coefficient. and so using that, these could be possible roots \[\pm \frac{ 1 }{ 1 } , ~ \pm \frac{ 1 }{ 3 } , ~ \pm \frac{ 2 }{ 1 } , ~ \pm \frac{ 2 }{ 3 } , ~ \pm \frac{ 3 }{ 1 } , ~ \pm \frac{ 3 }{ 3 } , ~ \pm \frac{ 6 }{ 1 } , ~ \pm \frac{ 6 }{ 3 } ~\]

AbdullahM
 one year ago
Best ResponseYou've already chosen the best response.0solve 3x1 = 0 x = 1/3 and since that is one of the possible roots, we can use that since it might be divisible by it.

AbdullahM
 one year ago
Best ResponseYou've already chosen the best response.0can someone explain? ;; this is hard to show online compared to inperson with a piece of paper ;;

AbdullahM
 one year ago
Best ResponseYou've already chosen the best response.0ik, but latex isn't that easy to use to show that ;; and the draw tool isn't that easy either ;;

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.0for long division 5 steps) \(\huge\color{green}{{1:}}\) Divide the first terms \(\huge\color{green}{{2:}}\) multiply(distribute) \(\huge\color{green}{{3:}}\) subtract all terms \(\huge\color{green}{{4:}}\) carry down \(\huge\color{green}{{5:}}\) repeat

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.0dw:1442023891316:dw divide first terms \[\huge\rm \frac{ 3x^3 }{ 3x } = ???\] then multiply the divisor with that

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.0^ divide first term of polynomial by first term of the divisor
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