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I've seen a number of criticisms of the article. Some things need to be kept in mind. Presently it is standard to introduce factoring before one knows how to

I've seen a number of criticisms of the article. Some things need to be kept in mind. Presently it is standard to introduce factoring before one knows how to graph polynomial functions. It is possible to argue that we teach this before factoring and I think a compelling case can be made for this but it isn't a standard practice. Anyone who thinks of using x-intercepts to explain this probably has had some College Algebra. The topic in the article is usually covered in Beginning Algebra. References to the discriminant in criticizing the article are not appropriate. The discriminant is taught after teaching factoring. The normal order of topics is 1. factoring 2. solving quadratic equations with factoring 3. proving the quadratic formula 4. solving general quadratic equations

czzarr 14y ago
Are you serious about college algebra? in France this is taught in middle school
- sp332 14y ago
  To be clear: yequalsx said Anyone who thinks of using x-intercepts to explain this probably has had some College Algebra. The topic in the article is usually covered in Beginning Algebra. So x-intercepts are taught in middle school, but the idea of using them to explain this particular problem probably wouldn't occur to someone with such little experience.
  - yequalsx 14y ago
    Indeed, college algebra students typically struggle when trying to tie in the concepts of factoring, x-intercepts, remainder theorem, and zeros of a polynomial. Lots of gnashing of teeth in this chapter.
- csense 14y ago
  "College algebra" is usually taken by people who haven't had algebra, geometry and trigonometry classes in middle or high school. If you had all those classes, many colleges allow you to enroll in calculus as a freshman (sometimes you have to take a placement test), or you can even skip some of the calculus sequence with AP credit. College algebra isn't something that a lot of math, science and engineering majors take, especially if they're toward the top of the class and haven't taken the easy road in their high school course selections.
louischatriot 14y ago
I would say that the discriminant method is taught at the same time as factoring, when we prove why this "b^2-4ac" is so interesting.
- yequalsx 14y ago
  You may say this but it is wrong to believe this. The discriminant is not taught when factoring is taught. Indeed, any quadratic can be factored over the complex numbers but this is beyond the students' mathematical prowess at the time we teach factoring. It's why we say to beginning algebra students that x^2 + 1 is prime but we show college algebra students that it can be factored over the complex numbers.
  - louischatriot 14y ago
    To clarify my comment above, I was talking about factorising 2nd order polynoms, which is taught at the same time as discriminant in France (I don't know about the way it is done in other countries). This makes sense as they are basically the same thing. What do you mean x^2+1 is prime ? For me prime only applies to integers or do I miss another way this word is used ?
    - yequalsx 14y ago
      Prime applies to objects in any commutative algebraic system that can't be further decomposed. I don't want to get too technical so I'm speaking in very loose terms. x^2+1 is prime over the integers but not over the complex numbers. I don't know the French education system but it would be very shocking to me if the discriminant is taught when factoring is first taught. Factoring x^3 - y^3 does not have anything to do with the discriminant and x^3 - y^3 is typically taught when factoring is first introduced. At least in the U.S.
      - R_Edward 14y ago
        x^2 + 1 is prime over the integers? Maybe they've changed math since I was in high school, but I'm pretty sure that, given n, such that n is an integer, if x = (2n + 1), then x^2 + 1 = 4n^2 + 4n + 2, which equals 2(2n^2 + 2n + 1), which is clearly not* prime.

czzarr 14y ago

Are you serious about college algebra? in France this is taught in middle school

sp332 14y ago
To be clear: yequalsx said Anyone who thinks of using x-intercepts to explain this probably has had some College Algebra. The topic in the article is usually covered in Beginning Algebra. So x-intercepts are taught in middle school, but the idea of using them to explain this particular problem probably wouldn't occur to someone with such little experience.
- yequalsx 14y ago
  Indeed, college algebra students typically struggle when trying to tie in the concepts of factoring, x-intercepts, remainder theorem, and zeros of a polynomial. Lots of gnashing of teeth in this chapter.
csense 14y ago
"College algebra" is usually taken by people who haven't had algebra, geometry and trigonometry classes in middle or high school. If you had all those classes, many colleges allow you to enroll in calculus as a freshman (sometimes you have to take a placement test), or you can even skip some of the calculus sequence with AP credit. College algebra isn't something that a lot of math, science and engineering majors take, especially if they're toward the top of the class and haven't taken the easy road in their high school course selections.

louischatriot 14y ago

I would say that the discriminant method is taught at the same time as factoring, when we prove why this "b^2-4ac" is so interesting.

yequalsx 14y ago
You may say this but it is wrong to believe this. The discriminant is not taught when factoring is taught. Indeed, any quadratic can be factored over the complex numbers but this is beyond the students' mathematical prowess at the time we teach factoring. It's why we say to beginning algebra students that x^2 + 1 is prime but we show college algebra students that it can be factored over the complex numbers.
- louischatriot 14y ago
  To clarify my comment above, I was talking about factorising 2nd order polynoms, which is taught at the same time as discriminant in France (I don't know about the way it is done in other countries). This makes sense as they are basically the same thing. What do you mean x^2+1 is prime ? For me prime only applies to integers or do I miss another way this word is used ?
  - yequalsx 14y ago
    Prime applies to objects in any commutative algebraic system that can't be further decomposed. I don't want to get too technical so I'm speaking in very loose terms. x^2+1 is prime over the integers but not over the complex numbers. I don't know the French education system but it would be very shocking to me if the discriminant is taught when factoring is first taught. Factoring x^3 - y^3 does not have anything to do with the discriminant and x^3 - y^3 is typically taught when factoring is first introduced. At least in the U.S.
    - R_Edward 14y ago
      x^2 + 1 is prime over the integers? Maybe they've changed math since I was in high school, but I'm pretty sure that, given n, such that n is an integer, if x = (2n + 1), then x^2 + 1 = 4n^2 + 4n + 2, which equals 2(2n^2 + 2n + 1), which is clearly not* prime.