logan saves the same amount of money each month for college. his current total savings is $300m^{2}+120m +…

logan saves the same amount of money each month for college. his current total savings is $300m^{2}+120m + 180$ dollars. which factorization could represent the number of months and amount of a monthly deposit in dollars?\n$4m(75m^{2}+30m + 40)$\n$10m(30m^{2}+12m + 18)$\n$30(10m^{2}+4m + 60)$\n$60(5m^{2}+2m + 3)$

logan saves the same amount of money each month for college. his current total savings is $300m^{2}+120m + 180$ dollars. which factorization could represent the number of months and amount of a monthly deposit in dollars?\n$4m(75m^{2}+30m + 40)$\n$10m(30m^{2}+12m + 18)$\n$30(10m^{2}+4m + 60)$\n$60(5m^{2}+2m + 3)$

Answer

Answer:

D. $60(5m^{2}+2m + 3)$

Explanation:

Step1: Find the greatest - common factor.

Find the GCF of 300, 120, and 180. The factors of 300 are $1,2,3,4,5,6,10,12,15,20,25,30,50,60,75,100,150,300$. The factors of 120 are $1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120$. The factors of 180 are $1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180$. The GCF of 300, 120, and 180 is 60.

Step2: Factor out the GCF.

$300m^{2}+120m + 180=60\times5m^{2}+60\times2m+60\times3=60(5m^{2}+2m + 3)$ So the factorization that could represent the number of months and amount of a monthly deposit is $60(5m^{2}+2m + 3)$.