Question

what is the factored form of the polynomial $27x^{2}y - 43xy^{2}$?
$\bigcirc\\ xy(27x - 43y)$
$\bigcirc\\ x^{2}y^{2}(27 - 43)$
$\bigcirc\\ 3xy(9x - 17y)$
$\bigcirc\\ 3x^{2}y(9 - 14y)$

Explanation:

Step1: Identify greatest common factor

The terms $27x^2y$ and $-43xy^2$ share the common factor $xy$. 27 and 43 have no common integer factors greater than 1.

Step2: Factor out the GCF

Divide each term by $xy$ and write as a product:
$27x^2y - 43xy^2 = xy(27x - 43y)$

Step3: Verify the result

Distribute $xy$ back: $xy \cdot 27x - xy \cdot 43y = 27x^2y - 43xy^2$, which matches the original polynomial.

Answer:

A. $xy(27x - 43y)$