Question

How do you factor `2x^(2/3) - 5x^(1/3) - 3 = 0`?

Answer 1

Well notice that `3=5-2` hence

#2x^(2/3) - 5x^(1/3) - 3 = 0=> 2x^(2/3)-5x^(1/3)-(5-2)=0=> 2*(x^(2/3)-1)-5(x^(1/3)-1)=0=> 2*(x^(1/3)+1)*(x^(1/3)-1)-5(x^(1/3)-1)=0=> (x^(1/3)-1)*[2(x^(1/3)+1)-5]=0#