1. ## Another polynomial questions

this is my problem:

Show that the order you group terms when factoring a four-term polynomial does ot nake any difference. Give one example to illustrate this, showing the steps of both situations. I will be sooo glad when this class is over...I'm sooo completly lost! I truly appreciate all the help this site has provided me!

2. Polynomial: $\displaystyle x^3 + 2x^2 - 4x - 8$

Case 1: Group together the first two and the last two:

$\displaystyle (x^3 + 2x^2) - (4x + 8)$

Which gives us:

$\displaystyle x^2(x + 2) - 4(x+2)$

We then have:

$\displaystyle (x^2 - 4)(x + 2)$

And since $\displaystyle (x^2 - 4)$ is a difference of squares we have:

$\displaystyle (x+2)(x-2)(x+2)$

Which equals:

$\displaystyle (x+2)^2(x-2)$

Case 2: Group the first with the third term and the second with the fourth:

$\displaystyle (x^3 - 4x) + (2x^2 - 8)$

Factor out common terms:

$\displaystyle x(x^2 - 4) + 2(x^2 - 4)$

Which gives us:

$\displaystyle (x + 2)(x^2 - 4)$

Once again, a difference of squares:

$\displaystyle (x + 2)(x + 2)(x - 2)$

$\displaystyle (x + 2)^2(x - 2)$