Comentario del Tutor: Elegí esta sesión ya que abarca un tema que no es muy usual de ver en Argentina , división de polinomios , por otro lado , en esta sesión el alumno no tenia un problema puntual para resolver , sino que necesitaba practica,  esto no es muy común , ya que normalmente los alumnos nos piden ayuda para resolver problemas particulares, a su vez trae una complicación , ya que se debe proveer un ejercicio adecuado al nivel del alumno , ni muy básico ni muy elevado . Por eso mismo en esta sesión comenzamos con un ejercicio simple , para comprobar que el alumno tuviese los conocimientos básicos necesarios , y luego optamos por resolver uno mas complicado , logrando que el alumno se esfuerce para resolver el ejercicio.

Student

I need help understanding division of polynomial a by monomials and polynomials.

Tutor

Welcome to Tutor.com ! My name is Javier . How are you ?

Student

Hello Javier. I am great. How are you?

Tutor

Im fine , thanks for asking :)

Student

Can you give me an example of a polynomial divided by a monomial and I will give it a shot?

Tutor

sure

x^5 +3x^3 + 4x^2 / x^2

Student

is that right?

Tutor

perfect ! :D

Student

Sweet. I am starting to understand them I think

how about division by a polynomial?

Tutor

ok lets try this one

x^3+2x^2 +x+1 / x+1

perfect :D

right !

and you have a remainder

Student

not for this one right?

oh yes I do

Tutor

mmm let me check something

oh thats right :)

because you erased the 1 now , that was confusing me :)

now its perfect !

Student

hmmmm. lets try one like that again that comes out with a remainder. I got a little iffy there at the end

Sweet

can we try another one that will come out with a remainder?

Tutor

ok

let me think another example

ok

4x^3 + 2x^2 + 5 / x-3

Student

How does that look?

Tutor

lets check that :)

dont forget the 5 :)

Student

ummm ok, lets back up. I’m confused

Tutor

sure

up to that step its perfect :D

Student

so in order to get 14x^2 I must multiply by 14x

Tutor

right

Student

now I switch the signs and add

Tutor

wait

we are doing 42x +5

we cannot add something with an X to something without an X , right ?

Student

oh, it just came to me…I needed a place holder

Tutor

right hehe

Student

may we start this over again

tricky little devil

:-)

Tutor

sure :)

Student

Thank you for throwing that in because I had forgotten all about that

Tutor

ok , lets start again :)

perfect !

wait please

how did the 5 transformed into 126 ?

oh sorry

Student

so in order to get 42x I must multiply by 42

Tutor

because of the 42 :)

yeah i missed that , sorry :)

continue please

Student

no problem

does that look right now?

Tutor

yes it does :)

its perfect :D

Student

OK, great

so I need to remember to watch out for the exponents

and use a place holder whenever needed

Tutor

right :D

do you have any questions about what we have covered today ?

Student

I think I am good for now. I need to practice a little more but I am starting to grasp this. Thank you so much for the help.

Have a nice evening!

Tutor

your welcome :)

Colaborador: Javier Verde, Tutor Argentino de Álgebra