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Can someone explain to me how to factor 9x² - 6x - 24?

Thanks!

 Jun 3, 2019
 #1
avatar+8756 
+3
___9x2 - 6x - 24____ 
  

 

 

Split  -6x  into two terms such that the product of their coefficients =  (-24)(9)  =  -216

What two numbers add to  -6  and multiply to  -216  ?→   +12  and  -18

=9x2 - 18x + 12x - 24

 

 

Notice here that if we combine like terms we get back the previous expression.
  

 

Factor  9x  out of the first two terms.
=9x(x - 2) + 12x - 24

 

 

Notice here that if we distribute  9x  we get back the previous expression.
  

 

Factor  12  out of the last two terms.
=9x(x - 2) + 12(x - 2)

 

 

Notice here that if we distribute  12  we get back the previous expression.
  

 

Factor  (x - 2)  out of both remaining terms.
=(x - 2)(9x + 12)  
   

We can factor  3  out of both terms in the second factor. We could have done this in the

beginning which would have made the numbers smaller.

=(3)(x - 2)(3x+4)  
 Jun 3, 2019
edited by hectictar  Jun 3, 2019

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