\({|3x^2 - 4x - 4|}\)
= \({3x^2 - 4x - 4}\)
= \({(x - 6)(x + 2)}\)
\(x = {6}\), \(x = {- 2}\)
however, the answer is \(x = -{2 \over 3}\), \(x = {2}\)
how?
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 .