123456
of 6

Freaky Factoring

YOUR TURN:

Factor:

14k^4 w + 56xk^3 w^2
 

14( x^2 - 3 )^4 ( 7x + 5 ) + 56x( x^2 - 3 )^3 ( 7x + 5 )^2


12x^2 w^6 y^3 + 12w^5 y^4


12x^2( 2x - 9 )^6 ( x^3 + 5 )^3 + 12( 2x - 9 )^5 ( x^3 + 5 )^4
 

The only other creepy thing that's going to happen with these is that some will have rational exponents...  fractions!  Not to worry though because they'll work the same way.  You just have to be able to pick which fraction is the smallest.

Let's start off easy:

Factory^4 x^( -1 / 2 ) + y^3 x^( 1 / 2 )

y^4 x^( -1 / 2 ) + y^3 x^( 1 / 2 ) = y^3 x^( -1 / 2 ) ( y + x )

The y's are easy... 
Which fraction power
is smaller?  That one
comes out!

 

That's it!  Multiply it back out if you don't believe me!