Everything You Need to Know About Factoring Quadratics
Intern
Joined: 17 Sep 2011
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Factoring quadratic equations [#permalink] 
02 Apr 2012, 18:06
Beloved all,
I'm having some problem with factoring quadratic equations, especially if the numbers get higher / more complex.
More specifically, I'm struggling with this quadratic equation:
t^ii+4t-672=0
this comes downward to
(t-24)(t+28)=0
Only I don't know how to go far at this solution in the most efficient way.
Would actually capeesh if someone could help me out here.
Thanks a lot!
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Joined: 06 Feb 2012
Posts: 86
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Re: Factoring quadratic equations [#permalink] 02 Apr 2012, 18:31
This thread was quite helpful because it has a lot of examples.
http://world wide web.purplemath.com/modules/factquad.htm
If x1 and x2 are the solutions to the quadratic equation and working backwards:
(x-x1)*(x-x2) = x^2 - (x1+x2) x + x1*x2
then you tin identify the terms of the developed form with the sum and product of the solutions.
In your specific example, I would decompose 672 knowing you lot desire to have a production of 2 terms
of contrary signs which adds upward to -iv
672=six*(112)=6*4*28=24*28
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Joined: 02 Sep 2009
Posts: 84748
Re: Factoring quadratic equations [#permalink] 03 Apr 2012, 00:06
jfk wrote:
Dear all,
I'm having some trouble with factoring quadratic equations, especially if the numbers get higher / more than complex.
More specifically, I'grand struggling with this quadratic equation:
t^2+4t-672=0
this comes down to
(t-24)(t+28)=0
But I don't know how to arrive at this solution in the most efficient way.
Would actually appreciate if someone could help me out here.
Thanks a lot!
Solving and Factoring Quadratics:
http://www.purplemath.com/modules/solvquad.htm
http://www.purplemath.com/modules/factquad.htm
Hope information technology helps.
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Re: Factoring quadratic equations [#permalink] 03 Apr 2012, 00:17
jfk wrote:
Dear all,
I'm having some trouble with factoring quadratic equations, especially if the numbers get higher / more circuitous.
More than specifically, I'm struggling with this quadratic equation:
t^two+4t-672=0
this comes downward to
(t-24)(t+28)=0
But I don't know how to get in at this solution in the nearly efficient way.
Would really appreciate if someone could help me out here.
Thanks a lot!
First, check out this mail:
hard-factoring-question-109006.html#p870223
Information technology discusses how to factor harder quadratic equations.
Coming to this question, yous accept -672 so the two factors which multiply to requite 672 will take opposite signs i.e. one of them volition be positive and the other will be negative. Also, their departure will be iv i.eastward. very minor.
Try and dissever 672 into its factors. We see that 672 is divisible by 4.
672 = 4*168 = 4*iv*42 = 4*4*2*iii*vii (We attempt to dissever the number till we get manageable factors)
At present you have to try various combinations of these factors till you get a pair with a deviation of iv. Notice that the divergence is very small and then we demand to get 2 factors which are kind of equal to each other. Say, ane factor can be 7*4 and some other can exist half dozen*4. 28 and 24 actually do take a difference of 4 and then nosotros accept got our 2 factors.
t^2 + 28t - 24t - 672 = 0
(t-24)(t+28) = 0
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Intern
Joined: 17 Sep 2011
Posts: 43
Re: Factoring quadratic equations [#permalink] 03 Apr 2012, 00:31
Thanks a lot everyone! Very helpful comments!
Intern
Joined: 26 Jun 2011
Posts: 8
Re: Factoring quadratic equations [#permalink] 05 Apr 2012, nineteen:31
Practice you need to solve this problem with paper and pen or can you employ a reckoner, programme, or website?
If you need an analytical solution, or pen-and-paper, another fashion to set on this blazon of problem would be to utilize the Quadratic Formula (QF); at that place is a lot of practiced material about the QF on Wikipedia or MathWorld. This arroyo is easier if you have a calculator, merely it allows for exact, algebraic, solutions.
On the other manus, if you lot cannot solve the problem easily, you might not have a option but to use the QF.
And if you are allowed to use a plan or web applet, then you tin can solve the problem numerically.
For example, hither is a free online applet that solves a Quadratic Equation:
Quadratic Equation Solver
Whether y'all use a spider web program, a full-diddled estimator program, or a pocket calculator, once you accept numeric solutions root1 and root2, yous could then re-land the original equation in the following form:
(t - root1)(t - root2)
If the roots are nice round numbers, that is nice merely doesn't always happen. The solutions are what they are.
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Re: Factoring quadratic equations [#permalink] 05 Apr 2012, 19:42
Quote:
Do yous demand to solve this trouble with paper and pen or can you utilise a calculator, plan, or website?
I'm pretty sure GMAC would pout upon any of the later on....
Intern
Joined: 26 Jun 2011
Posts: eight
Re: Factoring quadratic equations [#permalink] 05 Apr 2012, 19:55
nsspaz151 wrote:
I'yard pretty sure GMAC would frown upon whatever of the afterward....
Truthful. I forgot the overall context of these forums. I looked at the question by itself and simply gave a general answer.
In any case, if a solution cannot be establish quickly by inspection, I suppose the QF is the only way to go. Unless a person wants to make a bunch of guesses and promise they get lucky.
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Re: Factoring quadratic equations [#permalink]
04 Jul 2020, 06:50
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Everything You Need to Know About Factoring Quadratics
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