Question 328
<pre><font face = "courier new" size = 3>Hi I'm an older student and I have a problem I don't
understand. How would you solve polynomials by factoring?
This is the problem: 2x^4=16x^2. Thank You
<font color = "blue"><b>
                  2x<sup>4</sup> = 16x<sup>2</sup> 
First observe that both sides can be divided by 2. So we
can make it simpler by dividing both sides by 2
                   x<sup>4</sup> = 8x<sup>2</sup>
Get zero on the right side:
            x<sup>4</sup> - 8x<sup>2</sup> = 0
Factor out x<sup>2</sup> on the left side:
           x<sup>2</sup>(x<sup>2</sup> - 8) = 0
Set each of these factor = 0 separately and solve:
Setting first factor = 0
                    x<sup>2</sup> = 0
                    x = 0
Setting second factor = 0
               x<sup>2</sup> - 8 = 0
                   x<sup>2</sup> = 8
Take square roots of both sides</pre>
` ` ` ` ` ` ` ` ` ` ` ` ` _     
` ` ` ` ` ` ` ` ` ` x = ±<font face = "symbol">Ö</font>8 
Simplify radical:` ` ` ` `___ 
` ` ` ` ` ` ` ` ` ` x = ±<font face = "symbol">Ö</font>4·2  
` ` ` ` ` ` ` ` ` ` ` ` ` _ `_
` ` ` ` ` ` ` ` ` ` x = ±<font face = "symbol">Ö</font>4·<font face = "symbol">Ö</font>2
` ` ` ` ` ` ` ` ` ` ` ` ` `_
` ` ` ` ` ` ` ` ` ` x = ±2<font face = "symbol">Ö</font>2 
`
Edwin <font face="wingdings" size = 7 color = "red">J</font>