Question

1. $3x^2$, 10
2. $25x^2$, $25y$
3. $18m^2$, $24nm$

Explanation:

Assuming the problem is to find the greatest common factor (GCF) for each pair of terms:

Problem 14: \(3x^2\), \(10\)

Step1: Factor each term

Factor \(3x^2\): \(3x^2 = 3 \times x \times x\)
Factor \(10\): \(10 = 2 \times 5\)

Step2: Identify common factors

There are no common prime factors between \(3x^2\) and \(10\) (other than \(1\)).

Step1: Factor each term

Factor \(25x^2\): \(25x^2 = 25 \times x \times x\)
Factor \(25y\): \(25y = 25 \times y\)

Step2: Identify common factors

The common factor is \(25\) (since both terms have \(25\) as a factor).

Step1: Factor each term

Factor \(18m^2\): \(18m^2 = 2 \times 3 \times 3 \times m \times m\)
Factor \(24nm\): \(24nm = 2 \times 2 \times 2 \times 3 \times n \times m\)

Step2: Identify common factors

The common prime factors are \(2\), \(3\), and \(m\). Multiply them: \(2 \times 3 \times m = 6m\)

Answer:

\(1\)

Problem 16: \(25x^2\), \(25y\)