Question

1. which expression is equivalent to $24gh - 12g^{2}+18g$?

a) $6g(4h - 12g + 18)$
b) $12g(2h - 12g + 18)$
c) $6g(4h - 2g + 3)$
d) $12g(2h - g + 3)$

Explanation:

Step1: Find the GCF of coefficients

The coefficients are 24, -12, 18. GCF of 24,12,18 is 6. The common variable factor is \( g \) (lowest power of \( g \) is 1). So GCF is \( 6g \).

Step2: Factor out \( 6g \)

Divide each term by \( 6g \):
\( \frac{24gh}{6g} = 4h \), \( \frac{-12g^2}{6g} = -2g \), \( \frac{18g}{6g} = 3 \).
So \( 24gh - 12g^2 + 18g = 6g(4h - 2g + 3) \).

Answer:

C) \( 6g(4h - 2g + 3) \)