What is the greatest common factor of the following monomials?
6x^3, 18x^2, 24x^4
a) 6x
b) 6x^2
c) x^2
d) 3x^2
I think the answer is b
Right
Thank you Damon
To find the greatest common factor of the given monomials, we can first write each monomial as a product of its prime factors and variables raised to their respective exponents.
6x^3 = 2 * 3 * x * x * x
18x^2 = 2 * 3 * 3 * x * x
24x^4 = 2 * 2 * 2 * 3 * x * x * x * x
Next, we look for the common factors among the monomials. We want to find the highest power of each common factor that is present in all the monomials.
We can see that the common factors among all three monomials are 2, 3, and x. However, the greatest common factor will consist of the highest powers of these common factors.
The highest power of 2 that is present in all three monomials is 2^1.
The highest power of 3 that is present in all three monomials is 3^1.
The highest power of x that is present in all three monomials is x^2.
Therefore, the greatest common factor of 6x^3, 18x^2, and 24x^4 is 2 * 3 * x^2, which can be written as 6x^2.
So, you are correct! The answer is b) 6x^2.
To find the greatest common factor (GCF) of the given monomials, we need to determine the largest factor that is common to all three monomials.
Let's break down each monomial to its prime factors:
6x^3 = 2 * 3 * x * x * x
18x^2 = 2 * 3 * 3 * x * x
24x^4 = 2 * 2 * 2 * 3 * x * x * x * x
To find the common factors, we look for the factors that all three monomials share. In this case, the common factors are 2, 3, and x.
Now, let's find the highest power of each common factor:
2: It appears as 2, 2, and 2 in each monomial. To find the highest power, we take the minimum exponent of 2, which is 1 (from 2^1).
3: It appears as 3, 3, and also 3 in each monomial. Hence, the highest power of 3 is 1 (from 3^1).
x: It appears as x, x, and also x^4 in each monomial. Therefore, the highest power of x is 4.
To find the GCF, we multiply the highest powers of each common factor:
GCF = 2^1 * 3^1 * x^4 = 6x^4
Comparing this result with the given options, we can see that none of the options match. Therefore, the correct answer is none of the provided options.