Farina wrote:
Its tricky. Any easy explanation?
If you're comfortable factoring things where the "a" value is not 1, then you essentially just use x^1/3 as your standard x value and factor, and sort out the exponent at the end step. This is because (X^1/3)(x^1/3)=(X^2/3) (because you add the exponents like conventional numbers or fractions when multiplying the same bases raised to a power)
The trick to factoring when the "a" value is not 1 is multiplying the "a" and "c" values to determine what you are trying to make the component x values multiply to. For example, in the given problem we have a=3 b=2 c=-8
3 X -8 = -24
so we factor by finding what multiplies to -24 and adds to our "b" value of positive 2, namely 6 and -4
so then we substitute 2x (with our x in this case being x^1/3) for 6x and -4x which still add to positive 2. We can then factor by grouping and factoring out what we can.
so 3x^2 + 6x - 4x - 8 gets grouped like so:
(3x^2 + 6x) (-4x - 8)
then we factor out what we can leaving a common base inside the parenthesis (which is how you know you're on the right track)
3x(x+2)-4(x+2)
then you use what's in the parenthesis as one factor, and what's outside as the second
(x+2)(3x-4) and you're off to the races.
In the given problem, if you use x^1/3 instead of x it will factor the same but the answer will be correct. Hope this helped