(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) $$ x^{2}+7 x+12 $$

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UpStudy AI · Accepted Answer

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!
Here are the factored forms of the given quadratic expressions: 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. $$ x^{2} + 7x + 12 = (x + 3)(x + 4) $$

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