i want to learn factoring polynomial equation
Posted: Thu Apr 20, 2017 4:58 pm UTC
where do i start ?
Forums for the webcomic xkcd.com
Well, what do you know now? Lacking that basic information would cause me to suggest the first grade.monkey3 wrote:where do i start ?
doogly wrote:It also helps to practice polynomial long division. Like, what is 2x^3 + 3x^2 - x - 2 / x - 4 ?
For a second degree polynomial, assuming that it can be factored normally at all, the answer is yes. For higher degree polynomials using that technique you can get the first term. You can then use polynomial division to find the second term. That is, divide the original polynomial by the first factor.monkey3 wrote:can i work like this all the time ? is it always possible this way ?
Zohar wrote:I'm not sure if you're being deliberately unhelpful, deliberately obtuse, or you just missed the entire point.
Try it and see. in the end, it's about all the numbers. The simple cases have a coefficient of 1 for the x2 term (or can get there by factoring a constant out of the whole shebang), the less simple ones don't.monkey3 wrote:is it about the first number and the third number ?
is it about the second number and the third number ?
Yes. Factors are "things that are multplied together", Terms are "things that are added together. So you are taking a polynomial and breaking it into factors. One of the neat things about this is that if even one of those factors is zero, the whole shebang is zero. So, any value of x that makes one of the (newly found) factors zero, is called a root of the polynomial. It's a place where the graph crosses the x axis - i.e. where y, the value of the polynomial, equals zero.monkey3 wrote:The whole process of splitting up numbers like this is called factoring or factorization ?
The list that follows... that is of things you now understand, or things that you still don't get?monkey3 wrote:things i was able to narrow down ,
Yes, essentially. In the case of integers, it is to break it into other integers that multiply out to the given number (12 factors into 4x3 or 2x2x3). In the case of polynomials, it is to break it into lower order polynomials that multiply out to the given one (examples upthread).monkey3 wrote:’To factor’ means to break up into multiples.
Yes. They are the same. They are primarily useful in saving steps when reducing, although sometimes it's easier to just use the greatest obvious divisor repeatedly. (between 24 and 36, 12 is the greatest common divisor (24 is 2x12 and 36 is 3x12), but if you don't see that right away but recognize that 6 goes into both, you can divide by six to find that 24=4x6 and 36=6x6. From there, you'd recognize that 4 and 6 have a common divisor of 2... so now you have 24=2x2x6 and 36 is 3x2x6; the 2x6, or 12, is your greatest common divisor.monkey3 wrote:greatest common factor (same as greatest common divisor ?)
Oh, I doubt it, but those are the big ones. Many are special cases; there are as many special cases as there are cats - that is, more than you can skin in a lifetime. But most of those cases aren't all that special and will still succumb to a more general method.monkey3 wrote:is that all the methods out there ?