Question

Logan saves the same amount of money each month for college. His current total savings is 300m2 + 120m + 180 dollars. Which factorization could represent the number of months and amount of a monthly deposit in dollars? 4m(75m2 + 30m +40) 10m(30m2 + 12m +18) 30(10m2 +4m + 60) 60(5m2 +2m +3)

Answer 1

find comon factors

300m^2=2*2*3*5*5*m*m
120m=2*2*2*3*5*m
180=2*2*3*3*5


GCF=2*2*3*5=60
factor out 60

60(5m²+2m+3)

answer is last one

Answer 2

The factorization that is going to represent the number of months and amount would be  60(5m2 +2m +3)

To solve this, you have to use the common greatest factor

What is the greatest common factor?

This is the largest integer that is known to divide a set of whole numbers in a  way that there is no zero number.

Factors of 300m²

= 2x2x3x5x5xmxm

Factors of 120m

=2x2x2x3x5xm

Factors of 180

=2x2x3x3x5

The factors that are common to all the numbers are 2, 2, 3, 5

= 2x2x3x5

= 60

Therefore the factorization that would represent the savings equation is 60(5m² +2m +3)

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