How to factor a quadriatic?

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nico4213: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Mon Aug 20, 2007 3:54 am; Location: Sydney

How to factor a quadriatic?

by nico4213 » Mon Aug 20, 2007 4:26 am

This is in the correction of a problem, but I have troubles to factor and I would never have found the second line by myself....is there a method that makes it very easy to find it?

0=w^2-17w+60

0=(w-12)(w-5)

Thank you!

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Source: Beat The GMAT — Problem Solving | Mon Aug 20, 2007 4:26 am

erdnah: Senior | Next Rank: 100 Posts; Posts: 65; Joined: Tue Jun 12, 2007 12:57 am

by erdnah » Mon Aug 20, 2007 4:39 am

I don't know a very easy method...
The first factor plus added to the second factor is always the term in the middle (-5 + -12 = -17); the first factor multiplied with the second factor is always the last term in the basic equation (-12 * -5 = 60).

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kevincanspain: GMAT Instructor; Posts: 613; Joined: Thu Mar 22, 2007 6:17 am; Location: madrid; Thanked: 171 times; Followed by:64 members; GMAT Score:790

by kevincanspain » Sat Aug 25, 2007 10:18 am

Note that the two numbers were are looking for sum - 17 and yield a product of 60, which means that both are negative. As the product is 60, one of the numbers is going to be a multiple of 5

Kevin Armstrong
GMAT Instructor
Gmatclasses
Madrid

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veekay: Senior | Next Rank: 100 Posts; Posts: 54; Joined: Fri Aug 10, 2007 6:51 am

by veekay » Sat Aug 25, 2007 5:39 pm

Here is one of the method to factor it

•Make sure that the coefficient on the term is equal to 1. rewrite it so that the X^2 and x terms are on one side and the constant is on the other side. X^2 -10X + 9= 0 as X^2 –10X = -9
•Then take out (b/2)2 for e.g (-10/2)2 = 25
•Add that to both sides of eqn X^2 –10X + 25 = -9 + 25
•X^2 –10X +25 = 16
•(X – 5)^2 = 4^2
•X – 5 = 4, X = -9
•And X-5 = -4, X=1

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kevincanspain: GMAT Instructor; Posts: 613; Joined: Thu Mar 22, 2007 6:17 am; Location: madrid; Thanked: 171 times; Followed by:64 members; GMAT Score:790

by kevincanspain » Sun Aug 26, 2007 11:01 am

veekay wrote:Here is one of the method to factor it

•Make sure that the coefficient on the term is equal to 1. rewrite it so that the X^2 and x terms are on one side and the constant is on the other side. X^2 -10X + 9= 0 as X^2 –10X = -9
•Then take out (b/2)2 for e.g (-10/2)2 = 25
•Add that to both sides of eqn X^2 –10X + 25 = -9 + 25
•X^2 –10X +25 = 16
•(X – 5)^2 = 4^2
•X – 5 = 4, X = -9
•And X-5 = -4, X=1

Nice! You might as well use the quadratic formula.
I recommend learning to factor by inspection, as it will improve your computational skills

Kevin Armstrong
GMAT Instructor
Gmatclasses
Madrid