1. 36 = 6·6 and 42 = 6·7 have a common factor of 6.
... x⁴ and x² have a common factor of x²
The GCF is 6x².
The factorization is 36x⁴ -42x² = 6x²(6x² -7)
2. All coefficients are multiples of 4. All variable factors are multiples of x³.
The GCF is 4x³.
The factorization is 4x⁵ -8x⁴ -4x³ = 4x³(x² -2x -1)
3. The GCF of coefficients 6 and 15 is (15 mod 6) = 3, which is also a factor of the other coefficients. The lowest power of m, which is m² is also a factor of the other terms.
The GCF is 3m².
The factorization is 6m⁵ -15m⁴ -21m³ +27m² = 3m²(2m³ -5m² -7m +9)