factors of 12a are 3, 2, and a
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The prime factorisation is 2*2*3*a. So the factors are1, 2, 3, 4, 6, 12, a, 2a, 3a, 4a, 6a and 12a. I have no idea how you go from that list to "the" factor.
Re-ordering it : 13a - a -15b + 2b = 12a - 13b
To factor the expression 24AB, we need to identify the common factors of 24 and AB. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. Since AB has no common factors other than 1, the factors of 24AB are 1, 2, 3, 4, 6, 8, 12, 24, A, B, 2A, 3A, 4A, 6A, 8A, 12A, 24A, B, 2B, 3B, 4B, 6B, 8B, 12B, and 24B.
factor pair = 650,1 factor pair = 325,2 factor pair = 130,5 factor pair = 65,10 factor pair = 50,13 factor pair = 26,25
Assuming the missing signs are pluses, that would work out to a^3 + 12a^2 + 14a + 5
In a negative correlation as one factor is decreased, the other factor is increased.