need help with factoring quadratic equations

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Sergio.: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Tue Apr 05, 2011 8:12 am

by Sergio. » Wed Jun 08, 2011 3:06 am

Help me understand how to factor quadratic equations,
for example: x^2-3x+2=x(x-1)(x-2)
Can anyone explain please step by step how do i get x(x-1)(x-2) from x^2-3x+2?

Thanks

Sergio.

UPD: I think I got it by my self

need to find two numbers that will yield "2" after multiplying and "-3" after addition. Am I correct?

Last edited by Sergio. on Wed Jun 08, 2011 3:13 am, edited 1 time in total.

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Source: Beat The GMAT — Problem Solving | Wed Jun 08, 2011 3:06 am

cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Wed Jun 08, 2011 3:12 am

x^2-3x+2=x(x-1)(x-2)
correction: x^2-3x+2 = (x-1)(x-2)
(you wrote an extra x)
anyway a quadratic can be written as (x-a)(x-b) (where a and b are roots/solution)
= x^2 - (a+b)x+ab
Thus in any quadratic -1*coefficient of x is sum of roots and the constant term is product of roots.
also discriminant, d =b^2 - 4ac
if d>0 ->distinct and real roots
d=0 means perfect square (i.e. same real roots)
d<0 complex roots
for equation ax^2 + bx + c,
roots are (-b+root(d)) /2a and (-b-root(d)) /2a )

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Sergio.: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Tue Apr 05, 2011 8:12 am

by Sergio. » Wed Jun 08, 2011 3:18 am

ye you're right about an extra "x", my mistake.

The original equation was x^3-3x^2+2x so i factored x(x^2-3x+2)=x(x-1)(x-2) but I forgot to remove "x" from my post.

Thanks for your explanation.
I remember about the discriminant from school, but didn't remember about factoring to (x-...)(x-...)[/b]

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kanishkporwal: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Wed Sep 14, 2011 9:56 pm

by kanishkporwal » Thu Sep 29, 2011 12:08 am

the first thing you need to do is to break the middle term in 2 terms which equals to the multiplication of the first term & the Third term
lets see here
x^2-3x+2
x^2-2x-x+2
(x-2)(x-1) which is your answer

there are other methods also to solve these first is through Quadratic formula
which is x=(-bÂ±?(bÂ²-4ac))/(2a)
this will be helpful for imaginary solutions

the last method is to complete the square to get the solution

I hope you now know How to solve quadratic equations
If you still have some doubts check the link below

https://math.tutorvista.com/algebra/quad ... tions.html

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