The greatest common factors of the polynomials are given by the GCF
of the terms of the polynomials.
Responses:
The factorization of the given polynomials using the greatest common factors are;
1. 12·a - 27 = 3·(4·a - 9)
2. 16·k - 24 = 8·(2·k - 3)
3. 48·w² - 36·w = 12·w·(4·w - 3)
4. 75·x²·y - 120·x·y = 15·x·y·(5·x - 8)
5. 4·a³·b - 8·a²·b² + 2·a·b³ = (2·a·b)·(2·a² - 4·a·b + b²)
6. 30·m⁴·n³ - 12·m³·n² + 6·m²·n = (6·m²·n)·(5·m²·n² - 2·m·n + 1)
Which methods is used to find the GCF of polynomial expressions?
The Greatest Common Factor, GCF, is given by the largest number that
divide two or more numbers which is given as follows;
1. 12·a - 27
The GCF of 12 and 27 is 3
Factorizing the above expression gives;
2. 16·k - 24
The GCF of 16 and 24 is 8
Factorizing 16·k - 24 gives;
Factorizing, 16·k - 24 using the GCF is 8·(2·k - 3)
16·k - 24 = 8·(2·k - 3)
3. 48·w² - 36·w
The GCF 48 and 36 is 12
w is also a factor, which gives;
48·w² - 36·w = 12·w·(4·w - 3)
Factorizing, 48·w² - 36·w, using the GCFs is; 48·w² - 36·w = 12·w·(4·w - 3)
4. 75·x²·y - 120·x·y
The GCF of 75 and 120 is 15
x·y is also a factor of the given expression, which gives;
The factorization of using the GCFs is; 75·x²·y - 120·x·y = 15·x·y·(5·x - 8)
5. 4·a³·b - 8·a²·b² + 2·a·b³
The GCF of 4, 8, and 2 is 2
a·b is also a factor
Which gives;
2·a·b·(2·a² - 4·a·b + b²)
4·a³·b - 8·a²·b² + 2·a·b³ = (2·a·b)·(2·a² - 4·a·b + b²)
6. 30·m⁴·n³ - 12·m³·n² + 6·m²·n
The GCF of 30, 12, and 6 is 6
m²·n is also a factor, which gives;
30·m⁴·n³ - 12·m³·n² + 6·m²·n = (6·m²·n)·(5·m²·n² - 2·m·n + 1)
Learn more about GCF here:
https://brainly.com/question/2335639
