Impossible to understand factoring polynomials. : r/learnmath
2022年9月1日 · There are a few different approaches to factoring polynomials. The most basic version starts with looking at what happens if you expand out a factored expression and try to match things up. Let's look at x 2 +5x+6. Assume that we can factor it as (x+r)(x+s) for some values r and s. Expanding out, we get (x+r)(x+s)=x 2 +(r+s)x+rs. So if we could ...
Why is factoring polynomials so hard? : r/mathematics - Reddit
That's a hard question. Factoring quadratic polynomials, at least, is really easy. Just use the quadratic formula. Factoring cubic polynomials is much more involved; factoring quartic polynomials is pretty much as complicated as cubic polynomials, and factoring polynomials of higher powers is actually impossible, mathematically. At least this ...
Anyone else think there's way to much emphasis on factoring …
Edit: also factoring (easy, small degree polynomials) is fast, and we want them to eventually understand the fundamental theorem of algebra. The basic tricks for quadratics are also useful in higher order polynomials which we do want to get them working with eventually, in whatever capacity is possible for them.
[Algebra 2] Factoring polynomials, I don't get it at all
2017年6月10日 · Factoring a polynomial into irreducibles allows you to explain it's behavior. For polynomials, this mostly amounts to knowing where the roots are (where the polynomial is equal to zero) and what the multiplicities of those zeroes are. Factoring is hard to motivate at the high school level, but is central to almost all of higher mathematics.
Is there a list to go through when factoring polynomials? : r/math
2019年1月29日 · There is a general (if highly inefficient) algorithm for factoring 1-variable polynomials (with integer coefficients) over the integer ring. The rough idea is that if you want to factor a polynomial f(x) as g(x) h(x), then g(m) has to divide f(m) for each integer m.
Serious issues understanding how to factor polynomials.
2024年3月15日 · It is important for me in order to become a computer scientist. Mainly the issue I'm running into is how to handle the steps into factoring the polynomials. For example: 4m^2 - 4m - 8 This is a trinomial with leading coefficient of 4. The instructor expects me to reduce it to a binomial by factoring it like this: 4(m - 6)(m+2)
I cannot factor polynomials for the life of me : r/learnmath - Reddit
2019年3月29日 · Then, there is the factoring that comes from the binomial theorem. (x+y) 2 =x 2 +2xy+y 2, (x+y) 3 =x 3 +3x 2 y+3xy 2 +y 2. and so on. These are the basic patterns that appear in the factoring problems that are actually doable by hand. Unfortunately, small changes can make it difficult to recognize the pattern.
When are students introduced to factoring polynomials in your
2019年12月4日 · Introduced? Alg 1. However, IMO, students don’t get enough context for what factoring is for. I teach PreCalc now, and students have trouble making the connection with factoring as a means of solving, simplifying, changing between forms for graphing, when to use the quadratic formula, etc.
What is the purpose of factoring a polynomial?What is factoring?
2016年8月30日 · An intriguing thing about factoring... both for polynomials and for whole numbers, is that it is hard to factor, while the inverse process (say, going from (x - 1)(x + 1) to x 2 - 1) is sometimes tedious, but ultimately not so bad. Ultimately, this asymmetry of difficulty is the basis of all cryptographic systems we use.
How in the world do you factor polynomials intuitively?! - Reddit
2023年8月15日 · First of all, factoring polynomials is an extremely difficult problem, just like factoring integers into primes is very difficult. This is the basis of the RSA algorithm in cryptography. Regarding your example. r\simmonator gave an excellent explanation already. Here is another point of view. You found the roots of the polynomial to be -3/2 and ...