Thereby proving sort of the entire rationale behind the process ( at least algebraically.). The algebraic calculations were quite laborious looking, but they seemed to add-up to make equal value on both sides of the equation. These things were at the end of the final chapter of the book basically, so I doubt that I ever really studied these back in the day very thoroughly.The "proof" was just an algebraic reasoning which explained the right hand side of the equation, which equals to the original trinomial (ax^2+bx+c)
The textbook did not contain elaborate and rigorous proof of the factorization, but it began with some assumptions. I think the textbook gave a good explanation and reasoning for the idea about factoring quadratics. I had to look up my old high school math textbook (which I had stowed away in the garage). The method in post #9 does not need to make any such assumptions,or perform any such checks. Of course, one can employ the rational root theorem to check if that is the case. The factorization has to be one of the above only if the roots are rational. That's probably why he's a mentor and I'm not.
What Chestermiller was trying to get you to ask yourself is what will produce 6x 2, what will produce -35, and what combination will result in +11x. So putting all that together, there are only a total of 8 possibilities, which are: So that means that the second terms inside the parentheses look like either: And since it is -35, that means one of those integers (but not both) has to be negative. Nevertheless, the only ways to get 35 is to multiply 35 times 1, or multiply 7 times 5. Now looking at the -35 number, it's kind of conspicuous that 7 x 5 = 35. So that means that the first terms inside the parentheses looks like either: In order to get 6x 2, you can either multiply 6x times 1x, or you can multiply 3x times 2x. I'm sorry I cannot be more productive at this problem. Is there a better way to help in factoring? I was taught many years ago in high school to use the guessing-method of trying to find the factor.īut I was not very good at this technique. Greatest common factor does not apparently exist because of 11 is prime, and it's not factor of 6 and neither of -35 It can be seen that 11 is a prime number therefore factor cannot be found for 11, unless it is 1? (it was not apparently the "guessing inside the parenthesis" method) I looked at the hints section of the problem, but I could not understand the method by which the factorization was found.
One particular difficult polynomial was thus: factorize the polynomial.Īccording to khan academy this can yet be further factorized (in some manner) I did not understand the khan academy tips and hints. I tried to wrap my head around the factoring problems, but it did not go well. I did some refresher exercises in khan academy.
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