Factor the expression completely. Begin by factoring out the lowest power of each common factor. 16x-3/2 + 8x-1/2 + x1/2

Question

I believe the lowest power is -1/2 or -1. I am just not sure if I pull out an x as well.

Answer 1

Recall that xⁿx^m = x^n+m

 

Factor out the smallest power (x^-3/2) from each term:

 

16x^-3/2 + 8x^-1/2 + x^1/2 = x^-3/2(16 + 8x + x²)

 

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