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Mathematical Expression Editor
Please be aware! Xronos is very good at making sure the factored polynomial you
have entered is the same polynomial. It is less reliable to know if you have entered a
fully factored version of that polynomial. To be sure that your factored version is
fully factored, you should check two things:
Every factor is degree 1 or degree 2 polynomial (a linear expression or a
quadratic).
If the factor is a quadratic, then the discriminate () must be negative.
If it is Zero or positive, then that term can be factored further and you
should try to do so.
Note: This is using an experimental factoring validator. If you verified that your
answer should be correct and Xronos won’t take it, please email your instructor to
see if there is a problem.
1 :
Factor the following polynomial (hint: Using the Rational Root Theorem to get a
zero, then divide out the factor to reduce the polynomial)
Remember that the Rational Root Theorem says you want to find all the factors of
the constant (i.e. ) and all the factors of the leading coefficient (i.e. ) and
create a list of () every combination of a factor of divided by a factor of
.
Note that this is probably going to give you a long list! Unfortunately there really
isn’t a great way to know which of the factors to try first; so I would typically suggest
starting with the ones that are easiest to calculate... This is why the Rational Root
Theorem should always be a tool of last resort! It takes a long time, and it is really
inefficient, but sometimes it’s all you have. In this spirit, once you have found a zero
and factored it out using something like polynomial long division, make sure to start
over on the resulting polynomial in terms of factoring; with any luck you
won’t need to use RRT and can use some other technique (like grouping
or quadratic form). The goal is to use RRT as infrequently as possible!
2 :
Factor the following polynomial (hint: Using the Rational Root Theorem to get a
zero, then divide out the factor to reduce the polynomial)
Remember that the Rational Root Theorem says you want to find all the factors of
the constant (i.e. ) and all the factors of the leading coefficient (i.e. ) and
create a list of () every combination of a factor of divided by a factor of
.
Note that this is probably going to give you a long list! Unfortunately there really
isn’t a great way to know which of the factors to try first; so I would typically suggest
starting with the ones that are easiest to calculate... This is why the Rational Root
Theorem should always be a tool of last resort! It takes a long time, and it is really
inefficient, but sometimes it’s all you have. In this spirit, once you have found a zero
and factored it out using something like polynomial long division, make sure to start
over on the resulting polynomial in terms of factoring; with any luck you
won’t need to use RRT and can use some other technique (like grouping
or quadratic form). The goal is to use RRT as infrequently as possible!
3 :
Factor the following polynomial (hint: Using the Rational Root Theorem to get a
zero, then divide out the factor to reduce the polynomial)
Remember that the Rational Root Theorem says you want to find all the factors of
the constant (i.e. ) and all the factors of the leading coefficient (i.e. ) and
create a list of () every combination of a factor of divided by a factor of
.
Note that this is probably going to give you a long list! Unfortunately there really
isn’t a great way to know which of the factors to try first; so I would typically suggest
starting with the ones that are easiest to calculate... This is why the Rational Root
Theorem should always be a tool of last resort! It takes a long time, and it is really
inefficient, but sometimes it’s all you have. In this spirit, once you have found a zero
and factored it out using something like polynomial long division, make sure to start
over on the resulting polynomial in terms of factoring; with any luck you
won’t need to use RRT and can use some other technique (like grouping
or quadratic form). The goal is to use RRT as infrequently as possible!
4 :
Factor the following polynomial (hint: Using the Rational Root Theorem to get a
zero, then divide out the factor to reduce the polynomial)
Remember that the Rational Root Theorem says you want to find all the factors of
the constant (i.e. ) and all the factors of the leading coefficient (i.e. ) and
create a list of () every combination of a factor of divided by a factor of
.
Note that this is probably going to give you a long list! Unfortunately there really
isn’t a great way to know which of the factors to try first; so I would typically suggest
starting with the ones that are easiest to calculate... This is why the Rational Root
Theorem should always be a tool of last resort! It takes a long time, and it is really
inefficient, but sometimes it’s all you have. In this spirit, once you have found a zero
and factored it out using something like polynomial long division, make sure to start
over on the resulting polynomial in terms of factoring; with any luck you
won’t need to use RRT and can use some other technique (like grouping
or quadratic form). The goal is to use RRT as infrequently as possible!