find the GCF of 8x and 20x^3
is the answer 4 or 4x?
4 is a factor of both 8 and 20 but I am not sure about the x or the exponent. thank you.
4x, 20x^3 = 20 * x * x * x
8x = 4x * 2
20x^3 = 4x * 5x^2
thank you
You are welcome.
To find the greatest common factor (GCF) of two terms, you need to determine the largest common factor between the coefficients and the variables raised to their respective exponents.
Let's break down the given terms, 8x and 20x^3, into their prime factors:
Term 1: 8x
- The prime factorization of 8 is 2 * 2 * 2.
- The prime factorization of x is x.
Term 2: 20x^3
- The prime factorization of 20 is 2 * 2 * 5.
- The prime factorization of x^3 is x * x * x.
To find the GCF, we need to identify the common factors between the two terms. In this case, the only common factor is 2. However, we need to consider the variable as well.
Since x is a common factor, we can include it in the GCF. However, when it comes to the exponent, we always choose the smallest exponent when finding the GCF. In this case, x has an exponent of 1 in the first term and 3 in the second term.
So, the GCF of 8x and 20x^3 is 2x.
Therefore, the answer is not 4 or 4x; it is 2x.