<PRE><B>Question 175743</B>
&lt;pre&gt;&lt;font size = 4 color = &quot;indigo&quot;&gt;&lt;b&gt;
f(x) = x&lt;sup&gt;4&lt;/sup&gt; + x&lt;sup&gt;3&lt;/sup&gt; + 2x&lt;sup&gt;2&lt;/sup&gt; + 4x - 8

Factor by grouping. 
First rearrange the terms:

f(x) = x&lt;sup&gt;4&lt;/sup&gt; + 2x&lt;sup&gt;2&lt;/sup&gt; - 8 + x&lt;sup&gt;3&lt;/sup&gt; + 4x

Factor the first three terms
Factor x out of the last two

f(x) = (x&lt;sup&gt;2&lt;/sup&gt; + 4)(x&lt;sup&gt;2&lt;/sup&gt; - 2) + x(x&lt;sup&gt;2&lt;/sup&gt; + 4)

Factor out {x&lt;sup&gt;2&lt;/sup&gt; + 4)

f(x) = (x&lt;sup&gt;2&lt;/sup&gt; + 4)[(x&lt;sup&gt;2&lt;/sup&gt; - 2) + x]

Remove parentheses inside bracket

f(x) = (x&lt;sup&gt;2&lt;/sup&gt; + 4)[x&lt;sup&gt;2&lt;/sup&gt; - 2 + x]

Rearrange the terms in the bracket,
and change the bracket to parentheses:

f(x) = (x&lt;sup&gt;2&lt;/sup&gt; + 4)(x&lt;sup&gt;2&lt;/sup&gt; + x - 2)

Factor the second parentheses:

f(x) = (x&lt;sup&gt;2&lt;/sup&gt; + 4)(x + 2)(x - 1)

Now we set that = 0

(x&lt;sup&gt;2&lt;/sup&gt; + 4)(x + 2)(x - 1) = 0

Using the zero factor principle:

x&lt;sup&gt;2&lt;/sup&gt; + 4 = 0        x + 2 =  0         x - 1 = 0
    x&lt;sup&gt;2&lt;/sup&gt; = -4           x = -2             x = 1
     x = ą2i

The solutions are 2i, -2i, -2, and 1

Edwin&lt;/pre&gt;</PRE>