Solving Quadratic Equation Using Box Factoring

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SUMMARY

The discussion centers on solving the quadratic equation f(x) = 6x² + 9x - 6 using the Box Method for factoring. The user initially attempted to factor the equation as (6x - 3)(3x + 6), which incorrectly resulted in a leading term of 18x². The correct approach involves first factoring out the common factor of 3, leading to the equation being simplified to 3(2x² + 3x - 2) before applying the Box Method. This clarification resolves the user's confusion regarding the application of the method.

PREREQUISITES
  • Understanding of quadratic equations and their properties
  • Familiarity with factoring techniques, specifically the Box Method
  • Knowledge of the distributive property (FOIL method)
  • Ability to identify and factor out common factors in polynomials
NEXT STEPS
  • Study the process of factoring quadratics by extracting common factors
  • Learn more about the Box Method for factoring polynomials
  • Practice solving quadratic equations using different factoring techniques
  • Explore resources on polynomial identities and their applications
USEFUL FOR

Students learning algebra, educators teaching quadratic equations, and anyone seeking to improve their factoring skills in mathematics.

nordqvist11
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Homework Statement




f(x)=6x^2+9x-6

Where does this function intersect the x-axis (i.e. what are the roots or zeroes of f(x))?

Solve by factoring using the Box Method. When I use the method that is shown on this website http://www.purplemath.com/modules/factquad2.htm for this particular problem I end up with this as my factored down version of the equation.
(6x-3)(3x+6)
But that is wrong because I would end up with 18x^2 as my leading term instead of the 6x^2 (which is in the desired equation) when I FOIL them out.

My question is that does using the method on that website to factor down a quadratic work for this equation? If so, could someone tell me what I'm doing wrong.

Thanks :)

Homework Equations





The Attempt at a Solution


[PLAIN]http://5img.com/img836/4599/69quadproblem.jpg
 
Last edited by a moderator:
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Welcome to PF, nordqvist11! :smile:

Your equation looks like the last example on the page you mentioned.
It says there that you should take out the common factor first...
 
You're right it does :). Thanks a lot, I got a real headache because of that.
 

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