Question 768968
<font face="Times New Roman" size="+2">


One good way to determine if you did a problem correctly is to start with your answer and work backwards.


Using FOIL on *[tex \LARGE (x\ +\ 4)(x^2\ +\ 8)], you really only have to test the firsts and the lasts.  *[tex \LARGE x\ \cdot\ x^2\ =\ x^3\ \not=\ 8x^3] and *[tex \LARGE 4\ \cdot\ 8\ =\ 32\ \not=\ 56].  Thank you for playing; Johnny has some lovely parting gifts on your way out...


Start again.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 8x^3\ +\ 56x^2\ +\ 8x\ +\ 56]


All terms have a common factor of 8, so


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 8(x^3\ +\ 7x^2\ +\ x\ +\ 7)]


Regroup:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 8(x^3\ +\ x\ +\ 7x^2\ +\ 7)]


Collect the two binomials that share common factors:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 8\left(\left(x^3\ +\ x\right)\ +\ \left(7x^2\ +\ 7\right)\right)]


Factor *[tex \LARGE x] from the first binomial, and *[tex \LARGE 7] from the second:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 8\left(x\left(x^2\ +\ 1\right)\ +\ 7\left(x^2\ +\ 1\right)\right)]


Now factor out *[tex \LARGE x^2\ +\ 1]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 8\left(x^2\ +\ 1\right)\left(x\ +\ 7\right)]


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
<font face="Math1" size="+2">Egw to Beta kai to Sigma</font>
My calculator said it, I believe it, that settles it
<div style="text-align:center"><a href="http://outcampaign.org/" target="_blank"><img src="http://cdn.cloudfiles.mosso.com/c116811/scarlet_A.png" border="0" alt="The Out Campaign: Scarlet Letter of Atheism" width="143" height="122" /></a></div>
</font>