x-3/2+2x+X1/2

Guess = x(x-1/2+2+x)

To confirm your guess, you can expand it back out, do you get the original equation?

Spoiler:

Consider $a^m \times a^n = a^{m+n}$ and $a^m \div a^n = a^{m-n}$

Hello, zbest1966!

$\text{Factor: }\:x^{-\frac{3}{2}} +2x+x^{\frac{1}{2}}$

I believe the answer is: . $x^{-\frac{3}{2}}\left(1 + 2x^{\frac{5}{2}} + x^2\right)$

Consider: . $2a^5 + 3a^4 + 5a^2$

Answer: . $a^2(2a^3 + 3a^2 + 5)$

Don't we factor out the variable with the least exponent?

. . (I didn't say that properly, but I'm sure you follow.}