d. \( 12 a b \) 4 Use greatest common factor and the distributive property to write and equivalent in factored form. \( 20 g+24 h \) a. \( 4(g+h) \) b. \( g h(20+24) \) c. \( 4(5 g+6 h) \) d. \( 2(10 g+12 h) \)

To factor the expression \( 20g + 24h \) using the greatest common factor (GCF) and the distributive property, we first need to identify the GCF of the coefficients 20 and 24. 1. **Find the GCF of 20 and 24:** - The factors of 20 are: \( 1, 2, 4, 5, 10, 20 \) - The factors of 24 are: \( 1, 2, 3, 4, 6, 8, 12, 24 \) - The common factors are: \( 1, 2, 4 \) - The greatest common factor is \( 4 \). 2. **Factor out the GCF from the expression:** - We can rewrite \( 20g + 24h \) as: \[ 20g + 24h = 4(5g + 6h) \] Now, let's compare this with the provided options: a. \( 4(g+h) \) - This is incorrect because it does not match our factored form. b. \( gh(20+24) \) - This is incorrect because it does not represent the original expression correctly. c. \( 4(5g+6h) \) - This is correct as it matches our factored form. d. \( 2(10g+12h) \) - This is also correct because \( 2(10g + 12h) \) can be simplified to \( 20g + 24h \), but it is not the simplest factored form. Thus, the correct answer is: **c. \( 4(5g + 6h) \)**.