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How do you find the GCF of #7x^2, 15xy#?

Answer 1

Nova Allen

The GCF is #x#.

Let's factor the two statements:

#7x^2 = 7*x*x# #15xy = 3*5*x*y#

#:. x# is the Greatest (and only) Common Factor between the two expressions.

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Answer 2

Genesis Amaya

To find the greatest common factor (GCF) of two or more terms, we need to identify the highest power of each variable that appears in all the terms and the smallest coefficient present in all the terms.

For the terms (7x^2) and (15xy):

We look at the coefficients: 7 and 15.
We consider the variables: (x^2) and (xy).

The GCF of 7 and 15 is 1 because there are no common factors other than 1.

For the variables, (x^2) and (xy), we look at the powers of (x) that appear in both terms. The highest power of (x) that appears in both terms is (x^1).

Thus, the GCF of the variables is (x).

Combining the GCF of the coefficients and the variables, we get the GCF of (7x^2) and (15xy) as (1 \times x = x). Therefore, the GCF of (7x^2) and (15xy) is (x).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.