Which expressions have exactly two foctors? Choose ALL that apply. ny 2 \( 3(b-1) \) \( a+7 \) 4.n.n \( m^{2}+8 \)

To determine which expressions have exactly two factors, let's analyze each option: 1. **ny** - **Factors:** \( n \) and \( y \) - **Analysis:** This is already expressed as a product of two variables. - **Conclusion:** **Has exactly two factors.** 2. **2** - **Factors:** 1 and 2 - **Analysis:** As a constant, 2 is a prime number with only two distinct factors. - **Conclusion:** **Has exactly two factors.** 3. **\( 3(b-1) \)** - **Factors:** 3 and \( (b-1) \) - **Analysis:** This is a product of a constant and a binomial. - **Conclusion:** **Has exactly two factors.** 4. **\( a + 7 \)** - **Analysis:** This is a sum of two terms and cannot be factored into a product of two non-unit factors. - **Conclusion:** **Does not have exactly two factors.** 5. **4.n.n (interpreted as \( 4n^2 \))** - **Factors:** Can be written as \( (2n) \times (2n) \) or \( 4 \times n \times n \) - **Analysis:** This expression can be factored in multiple ways, involving more than two factors when broken down further. - **Conclusion:** **Does not have exactly two factors.** 6. **\( m^2 + 8 \)** - **Analysis:** This is a sum of squares (since 8 is not a perfect square) and cannot be factored into a product of two binomials over the integers. - **Conclusion:** **Does not have exactly two factors.** **Final Answer:** - **ny** - **2** - **\( 3(b-1) \)** These three expressions each have exactly two factors.