(picture) factoring polynomials: gcf !

GCF is 5m^2 n^2

m^2 has exponent 2  and n^2 has exponent 2

(1) m^5n^5

here there is no 5 so it does not have GCF

(2) 5m^4n^3

m^4 has exponent 4 greater than exponent 2

n^3 has exponent 4 greater than exponent 2

5m^4n^3 have GCF

(3) 10m^4n

10 is 5*2 . it has GCF 5

m^4 has exponent 4 greater than exponent 2

n has exponent 1 less than exponent 2

10m^4n does not have GCF

(4) 15m^2n^2

15 is 3*5 which has GCF 5

m^2 has exponent 2 which is equal to exponent 2

n^2 has exponent 2 which is equal to exponent 2

15m^2n^2 have GCF

(5) 24m^3n^4

24 is 2*2*2*3 does not have GCF

m^3 has exponent 3 greater than exponent 2

n^4 has exponent 4 greater than exponent 4

24m^3n^4 does not  have GCF

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18

answer is 33

step-by-step explanation: