4chan archive /sci/ (index)
2012-09-06 05:29 5031423 Anonymous (1343198813206.gif 354x372 239kB)
I have a concerning issue with math, as I am just starting to take this recreational interest seriously. Two examples have stumped me and my sense of intuition. 1st one is simple: 4x^2 + 25x - 21 Two things that are necessary to factorize this are a+b = 25, and ab = (4)(-21) so you end up with (4x^2 + 28x) + (-3x - 21) Intuition is easy in an example like x^2 + 7x + 10, where ab = 10 and a+b = 7, but how do you know in the previous example that ab must equal 4x^2 and the constant -21? Trial and error? Second: f(x) = ax^3 + bx^2 + cx + d zeroes: (4,0) (-2,0) (6,0) y-intercept: (0,-5) f(x) = a(x-4)(x+2)(x-6) If you assign x the value of 0, it will cancel the entire thing, I get that. But is this the only property that lead one man to say "This must be another form of expressing f(x) = ax^3 + bx^2 + cx + d!!"? This somehow takes away my intuition since you are taking one part of the original equation and utilizing known values along the axes (3 of them along x, so you use ax^3). What's you intuition on this? I guess my broader question is: does intuition start to escape from you as you move on to polynomials? Does it become more of a systematical, methodological trial and error as you progress into more theoretical math?

2 min later 5031427 Anonymous
>>5031423 Oops. Correction: "...but how do you know in the previous example that ab must be the the product of 4 and the constant -21? Trial and error? Why not other operations?"

28 min later 5031449 Anonymous
Nobody? I thought this would've been a question many people would be more than happy to answer..

48 min later 5031487 Anonymous
I've perhaps came to a thread of egotism where showcasing one's ability to answer direct practical questions overpowers answering any genuine question much relevant to the basis of understanding and improving in math. Thanks anyway. I will browse elsewhere.

54 min later 5031505 Anonymous
>>5031423 Unless you can just see the factors right away, factoring is usually trial and error

1 hours later 5031549 Anonymous
>>5031423 Polynomials are actually very theoretic. If you have three roots over the real numbers, for instance, I don't actually intuitively think of a third degree polynomial. I just think that you could have a 3 + 2n degree polynomial, where n is some natural number and the 2n term is the number of complex roots of the polynomial. I hope for a third degree, but often times it's just a matter of seeing what's in front of you and using what you know to try and solve a problem and figure out more tools to solve more problems.

0.673 0.033