How do you factor x^(-1/2) - 2x^(1/2) + x^(3/2)?

1 Answer
MathFact-orials.blogspot.com
Feb 26, 2017

x^(-1/2)(x-1)^2=(x-1)^2/x^(1/2)=(x^(1/2)(x-1)^2)/x

Explanation:

Normally, when dealing with a trinomial, we're looking for something that looks like:

ax^2+bx+c

and our question doesn't have that! What it does have, however, if we compare the c term in what we are normally looking for to the x^(-1/2) in the question, the difference is the (-1/2) exponent. And, in fact, all the terms in the question have that same difference between what we expect over what we have. So let's first factor out a x^(-1/2) term:

x^(-1/2)-2x^(1/2)+x^(3/2)

x^(0-1/2)-2x^(1- 1/2)+x^(4/2-1/2)

x^0 xx x^(-1/2)-2x xx x^(-1/2)+x^2 xx x^(-1/2)

x^(-1/2)(1-2x+x^2)

and now we can factor in the normal way:

x^(-1/2)(x^2-2x+1)

x^(-1/2)(x-1)^2=(x-1)^2/x^(1/2)=(x^(1/2)(x-1)^2)/x

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