3) \( x^{2}-6 x+5 \) 4) \( x^{2}-5 x+6 \) 5) \( x^{2}-5 x-6 \) 6) \( x^{2}-x-6 \)

Certainly! Let's factor each of the given quadratic expressions. ### 3) \( x^{2} - 6x + 5 \) **Objective:** Factor the quadratic expression. **Method:** 1. Look for two numbers that multiply to **+5** (the constant term) and add up to **-6** (the coefficient of \( x \)). 2. The numbers are **-1** and **-5** because: - \((-1) \times (-5) = +5\) - \((-1) + (-5) = -6\) **Factored Form:** \[ x^{2} - 6x + 5 = (x - 1)(x - 5) \] --- ### 4) \( x^{2} - 5x + 6 \) **Objective:** Factor the quadratic expression. **Method:** 1. Look for two numbers that multiply to **+6** and add up to **-5**. 2. The numbers are **-2** and **-3** because: - \((-2) \times (-3) = +6\) - \((-2) + (-3) = -5\) **Factored Form:** \[ x^{2} - 5x + 6 = (x - 2)(x - 3) \] --- ### 5) \( x^{2} - 5x - 6 \) **Objective:** Factor the quadratic expression. **Method:** 1. Look for two numbers that multiply to **-6** and add up to **-5**. 2. The numbers are **-6** and **+1** because: - \((-6) \times (+1) = -6\) - \((-6) + (+1) = -5\) **Factored Form:** \[ x^{2} - 5x - 6 = (x - 6)(x + 1) \] --- ### 6) \( x^{2} - x - 6 \) **Objective:** Factor the quadratic expression. **Method:** 1. Look for two numbers that multiply to **-6** and add up to **-1**. 2. The numbers are **-3** and **+2** because: - \((-3) \times (+2) = -6\) - \((-3) + (+2) = -1\) **Factored Form:** \[ x^{2} - x - 6 = (x - 3)(x + 2) \] --- **Summary of Factored Forms:** 1. \( x^{2} - 6x + 5 = (x - 1)(x - 5) \) 2. \( x^{2} - 5x + 6 = (x - 2)(x - 3) \) 3. \( x^{2} - 5x - 6 = (x - 6)(x + 1) \) 4. \( x^{2} - x - 6 = (x - 3)(x + 2) \) If you need further assistance or have more questions, feel free to ask!