Find the greatest common monomial factor of the following terms:
1.3a,6ab²,12b²
2.32mn²,12m²n²,28mn
3.30c²d,20d,50d³
#1. 3a is clearly the only common factor
#2 GCF(32,12,28) = 4, so 4mn
#3 GCF(30,20,50) = 10, so 10d
mathematics
Polynomial:27d⁴o³t³a6-18d²o³t6-15d6o⁴
Quotient of polynomial and CMF:9d²o²t³a6-6t6-5d⁴
What is factor form and CMF?
To find the greatest common monomial factor of a set of terms, we need to determine the highest power of each variable that appears in all the terms.
1. For the terms 1.3a, 6ab², 12b²:
To find the greatest common monomial factor, we look for the highest power of each variable that appears in all the terms.
- For 'a': The term 1.3a contains a, but the other two terms do not. Therefore, the highest power of 'a' is 1.
- For 'b': The second and third terms, 6ab² and 12b², contain b but the first term, 1.3a, does not. The highest power of 'b' is 2.
The greatest common monomial factor is 1a²b².
2. For the terms 32mn², 12m²n², 28mn:
- For 'm': The second and third terms, 12m²n² and 28mn, contain m, but the first term, 32mn², does not. The highest power of 'm' is 1.
- For 'n': All three terms, 32mn², 12m²n², and 28mn, contain n. The highest power of 'n' is 1.
The greatest common monomial factor is 1mn.
3. For the terms 30c²d, 20d, 50d³:
- For 'c': The first term, 30c²d, contains c, but the other two terms do not. The highest power of 'c' is 2.
- For 'd': All three terms, 30c²d, 20d, and 50d³, contain d. The highest power of 'd' is 1.
The greatest common monomial factor is 1c²d.