Why is it useful to factor out the gcf first when factoring? (for example: 4x2 + 8x – 32)

It's useful to divide out the GCF first because it makes factoring easier as the coefficients are smaller requiring less steps. 

Example where you don't factor GCF first...
4*-32 = -128
numerous factor pairs for 128 ... takes time to find the correct one
right factor pair is 16,-8
substitute for 8x
4x² + 16x - 8x - 32 = 0
group then factor
4x(x+4) - 8(x+4) = 0
group again
(4x-8)(x+4) = 0

Example of factoring GCF first
4x² + 8x - 32 = 0
4 is GCF
x² + 2x - 8 = 0
factor
(x+4)(x-2) = 0

Solving for x gives the same answer just less steps and simpler math when you factor GCF first.

The slope best fit isc. 1/6 mile per hour

Ibelieve it's a. 2.2 - x = -10.85 (plz tell me if it's right : ) )