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\({|3x^2 - 4x - 4|}\)

\({3x^2 - 4x - 4}\)

\({(x - 6)(x + 2)}\)

\(x = {6}\)\(x = {- 2}\)

 

however, the answer is \(x = -{2 \over 3}\)\(x = {2}\)

how?

 Apr 30, 2018
 #1
avatar+7352 
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Let's check your factoring by multiplying out  (x - 6)(x + 2) :

 

(x - 6)(x + 2)  =  (x)(x) + (x)(2) + (-6)(x) + (-6)(2)

                      =  x2 + 2x - 6x - 12

                      =  x2 - 4x - 12

 

 x2 - 4x - 12   is not the same as  3x2 - 4x - 4  ,  so

(x - 6)(x + 2)  is not the same as  3x2 - 4x - 4

 

We can factor  3x2 - 4x - 4  like this....

 

3x2 - 4x - 4   What two numbers add to  -4  and multiply to  -12 ?   -6 and +2
  So we can split  -4x  into two terms like this...
   
=  3x2 - 6x + 2x - 4

 

Notice that if we combined  -6x  and  +2x  we would get  -4x  again.
  Factor  3x  out of the first two terms.
   
=  3x(x - 2) + 2x - 4

 

Notice here that if we distributed the  3x  we'd get the last expression.
  Factor  2  out of the last two terms.
   
=  3x(x - 2) + 2(x - 2)

 

Again, if we distributed the  2  we would get the last expression.
  Factor  (x - 2)  out of both remaining terms.
   
=  (x - 2)(3x + 2)  

 

So   3x2 - 4x - 4  =  (x - 2)(3x + 2)

 

To find the  x  values that make the expression equal to zero, set  (x - 2)(3x + 2)  equal to  0 .

 

(x - 2)(3x + 2)  =  0      Set each factor equal to zero and solve for  x .

 

x - 2  =  0       or       3x + 2  =  0

   x  =  2         or          x  =  -2/3

 

So the  x  values that make  3x2 - 4x - 4  equal zero are  x = 2  and  x = -2/3 .

 Apr 30, 2018
edited by hectictar  Apr 30, 2018

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