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# factoring this trinomial?

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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

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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