Question

Find the greatest common facter of these three expressions. 42v²,12v, and 18v⁴

Answer 1

The GCF of 42v², 12v, and 18v⁴ is 6v, which is found by determining the greatest common factor of the numeric coefficients (6) and the smallest power of the variable v present in all expressions.

Step-by-step explanation:

The student is asking to determine the greatest common factor (GCF) of the three algebraic expressions 42v², 12v, and 18v⁴. To find the GCF of algebraic expressions, we look for the highest power of variables that is common to all terms as well as the greatest common factor of the numeric coefficients.

Steps to Find the GCF

1. First, we find the GCF of the numeric coefficients, which are 42, 12, and 18.
2. The GCF of 42, 12, and 18 is 6, since that is the largest number that divides each of them without a remainder.
3. Next, we consider the variable part of the expressions. Since the variable is v and the smallest power of v that is in each term is simply v the GCF is v.

Hence, the GCF of 42v², 12v, and 18v⁴ is 6v.

Answer 2

The greatest common factor of the expressions 42v², 12v, and 18v⁴ is 6v.

Step-by-step explanation:

The greatest common factor (GCF) of the expressions 42v², 12v, and 18v⁴ can be found by finding the common factors among the terms. First, let's break down each term into its prime factors:

1. 42v² = 2 × 3 × 7 × v × v
2. 12v = 2 × 2 × 3 × v
3. 18v⁴ = 2 × 3 × 3 × v × v × v × v

Now, let's find the common factors among the terms. We can see that the factors 2, 3, and v are common to all three terms. Therefore, the GCF is 2 × 3 × v = 6v.