all you smart math ppl - Factoring Help?

Question

Actually, I don't have anything for you guys to solve... but I'm just wondering. When you factor a quadratic equation... where you have no choice but to guess and check... is there an easy way to factor w/o that guess & check crap.
Some of the people in my class know how to do it... and I want to know...

For example, factor:
(5x^2 - 19x - 4). I know the answer is
(5x+1)(x-4). But I had to do that... list thing and test it out.

btw i'm not looking for the quadratic formula... i'm not looking for what x equals...

hmm.. what's that diamond method?

i'll accept all types of methods...

what i heard from my teacher is that she hates using that "method" b/c it has several steps... but some of my classmates say it's pretty useful

Answer 1

There are clues to help you, but it still requires some guess-and-check- you just get fewer choices. For example if the middle number is large, like here, you know that the first and last have to be big and the outer and inner have to be small. You know that if the original terms of the trinomial had no common factors, then the two binomials won't either. So (2x-4) for example would never be a factor, so don't waste time guessing it. You can guess the signs (but may have to reverse them) by looking at the signs in the trinomial: both plus means both plus; minus then plus means both minus; plus then minus means one of each; both minus means one of each.

Answer 2

This is what I would probably do.
1. Look at the equation. Factor out to simplify.
ex. 5x^2+5x+5 = 0, factor out 5 first
2. Look at your coefficients. The 2 on the ends, record all the factors of those. For the ones in the middle, think of what adds/subtracts to get those (using the factors just recorded)
3. Try to look at the equation from different angles. Play around with it a little by separating it or rearranging. Have a little fun with it then get back to work.

Answer 3

well for a problem like this its really easy because the first number is odd (5) and the last number (4) only have two different pairs for products (1 and 4, 2 and 2) and for this problem it ended up being 1 and 4. but for a problem that has bigger numbers concluding it to have more factor pairs there is a way but i don't know your math level so you might not know how to do it. and to tell you the truth, i don't remember how to do it because i rarely used it but there is also a different way that i sometimes used which was the quadratic formula. once again i don't know your math level so i don't know if you're familar with that or not. i just guess and check and i think it's the fastest way to go.

Answer 4

Use the slide method.
Take the coefficent of x^2 and multiply it with the last number:
x2 - 19x - 20
Then factor that:
(x + 1) (x - 20)
Then, divide both numbers by the coefficient you got rid of earlier:
(x + 1/5)(x - 20/5)
Denominator after division (if the division is clean, that is) goes in front of the x:
(5x+1) (x -4)

I hope that made sense. If not, email me at [e-mail] or google slide method. I'm sure it's online somewhere.

Answer 5

of direction I are smart! I be superminion! Superminion be authentic reliable smart! I made this type of fool of myself contained in the maths section when I first began using Y!A, i have not been decrease back in view that. purely blithely wrote the answer, moved on, checked decrease back after the perfect answer became chosen, and idea... oh. truly. I wrote that, huh? follow books and technology, superminion, purely go away the maths on my own. sensible, I impressive my solutions if that's no longer too late, yet each and every from time to time I purely should be happy no one right that's conscious of my finished call. Worse is when I do it in human being, like the verbal substitute i became having the different day about Microsoft operating platforms. I freely admit that i comprehend no longer something about computers, yet to no longer even understand Microsoft wasn't layered severe of MS-DOS anymore? So, so unhappy. in my opinion i'm stimulated that you comprehend something about heritage. Technically, I studied heritage in college. Yep. sensible. It became myself and a couple of acquaintances wandering around the school, getting semi-annual telephone calls from our Distance preparation instructor. "wager what, females, you've an exam immediately! you've all studied, perfect?" Uh, perfect.

Answer 6

there's a thing called the quadratic formula. it's x=(-b+/-sqrt(b^2-4ac))/2a where (in your example) a=5, b=-19, and c=-4. so x=(19+/-sqrt(19^2-4*5*-4))/2*5
x=(19+/-sqrt(361+80))/10
x=(19+/-sqrt(441))/10
x=(19+/-21)/10
x=40/10 or x=-2/10 which would give you (x-4) and (x+1/5) or (5x+1)

Answer 7

try this page http://jtaylor1142001.net/calcjat/Courses/Ma99/ProgInstr/8QuadFctsEqns/2FactorSqrRoot/FReadme.htm

just by looking at most should be enough to factor them
i think some teachers teach a diamond method but i dont like it and find it a waste of time. i didnt learn it so i cant explain it