Question

factor ( 25x^{-3}y + 52x^5 - 39x^{-2} ). what is the resulting expression?
a) ( 123x^{-3}(y + 4x^5 - 3x^{-2}) )
b) ( 123x^{-3}(2x - 4x^5 - 3x^2) )
c) ( 123x^{-3}(2x + 4x^5 - 3x^2) )
d) ( 123x^{-3}(25x^{-3}y + 52x^5 - 39x^{-2}) )

Explanation:

Step1: Identify GCF of coefficients

The coefficients are 25, 50, 25. Their greatest common factor (GCF) is 25.

Step2: Identify GCF of $x$-terms

The $x$-terms are $x^3$, $x^5$, $x^3$. The GCF is $x^3$.

Step3: Factor out overall GCF

Factor $25x^3$ from each term:
$25x^3y - 50x^5 - 25x^3y^2 = 25x^3(y - 2x^2 - y^2)$

Answer:

$\boldsymbol{25x^3(y - 2x^2 - y^2)}$ (matches the second option, assuming formatting clarity for the options provided)