(1) \( x^{2}-11 x+28 \) (4) \( x^{2}-4 x-12 \) (7) \( a^{2}-12 a+35 \) (10) \( m^{2}-5 m-6 \) (13) \( x^{2}+7 x+12 \)

Sure, let's factor each of the given quadratic expressions: ### (1) \( x^{2} - 11x + 28 \) **Factorization:** We need two numbers that multiply to **28** and add up to **-11**. These numbers are **-4** and **-7**. \[ x^{2} - 11x + 28 = (x - 4)(x - 7) \] --- ### (4) \( x^{2} - 4x - 12 \) **Factorization:** We need two numbers that multiply to **-12** and add up to **-4**. These numbers are **-6** and **+2**. \[ x^{2} - 4x - 12 = (x - 6)(x + 2) \] --- ### (7) \( a^{2} - 12a + 35 \) **Factorization:** We need two numbers that multiply to **35** and add up to **-12**. These numbers are **-5** and **-7**. \[ a^{2} - 12a + 35 = (a - 5)(a - 7) \] --- ### (10) \( m^{2} - 5m - 6 \) **Factorization:** We need two numbers that multiply to **-6** and add up to **-5**. These numbers are **-6** and **+1**. \[ m^{2} - 5m - 6 = (m - 6)(m + 1) \] --- ### (13) \( x^{2} + 7x + 12 \) **Factorization:** We need two numbers that multiply to **12** and add up to **+7**. These numbers are **+3** and **+4**. \[ x^{2} + 7x + 12 = (x + 3)(x + 4) \] --- **Summary of Factorizations:** 1. \( x^{2} - 11x + 28 = (x - 4)(x - 7) \) 2. \( x^{2} - 4x - 12 = (x - 6)(x + 2) \) 3. \( a^{2} - 12a + 35 = (a - 5)(a - 7) \) 4. \( m^{2} - 5m - 6 = (m - 6)(m + 1) \) 5. \( x^{2} + 7x + 12 = (x + 3)(x + 4) \) If you have any further questions or need additional assistance, feel free to ask!