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The image contains several quadratic expressions. It appears these expressions are intended for factoring. I will solve each problem by factoring the quadratics. Here's the detailed solution:

### Solutions:

**13)** \( b^2 - 6b + 8 \)  
To factor this:
1. Find two numbers that multiply to \( 8 \) and add to \( -6 \). These numbers are \( -4 \) and \( -2 \).
2. The factorized form is:  
   \[ (b - 4)(b - 2) \]

**14)** \( n^2 + 6n + 8 \)  
1. Find two numbers that multiply to \( 8 \) and add to \( 6 \). These numbers are \( 4 \) and \( 2 \).
2. The factorized form is:  
   \[ (n + 4)(n + 2) \]

**15)** \( 2n^2 + 6n - 108 \)  
1. Factor out the greatest common factor (GCF), which is \( 2 \):
   \[ 2(n^2 + 3n - 54) \]
2. Now, find two numbers that multiply to \( -54 \) and add to \( 3 \). These numbers are \( 9 \) and \( -6 \).
3. The factorized form is:  
   \[ 2(n + 9)(n - 6) \]

**16)** \( 5n^2 + 10n + 20 \)  
1. Factor out the GCF, which is \( 5 \):
   \[ 5(n^2 + 2n + 4) \]
2. The expression \( n^2 + 2n + 4 \) cannot be factored further using integers. Thus, it remains:
   \[ 5(n^2 + 2n + 4) \]

**17)** \( 2k^2 + 22k + 60 \)  
1. Factor out the GCF, which is \( 2 \):
   \[ 2(k^2 + 11k + 30) \]
2. Find two numbers that multiply to \( 30 \) and add to \( 11 \). These numbers are \( 6 \) and \( 5 \).
3. The factorized form is:  
   \[ 2(k + 6)(k + 5) \]

**18)** \( a^2 - a - 90 \)  
1. Find two numbers that multiply to \( -90 \) and add to \( -1 \). These numbers are \( -10 \) and \( 9 \).
2. The factorized form is:  
   \[ (a - 10)(a + 9) \]

**19)** \( p^2 + 11p + 10 \)  
1. Find two numbers that multiply to \( 10 \) and add to \( 11 \). These numbers are \( 10 \) and \( 1 \).
2. The factorized form is:  
   \[ (p + 10)(p + 1) \]

**20)** \( 5v^2 - 30v + 40 \)  
1. Factor out the GCF, which is \( 5 \):
   \[ 5(v^2 - 6v + 8) \]
2. Find two numbers that multiply to \( 8 \) and add to \( -6 \). These numbers are \( -4 \) and \( -2 \).
3. The factorized form is:  
   \[ 5(v - 4)(v - 2) \]

**21)** \( 2p^2 + 2p - 4 \)  
1. Factor out the GCF, which is \( 2 \):
   \[ 2(p^2 + p - 2) \]
2. Find two numbers that multiply to \( -2 \) and add to \( 1 \). These numbers are \( 2 \) and \( -1 \).
3. The factorized form is:  
   \[ 2(p + 2)(p - 1) \]

**22)** \( 4v^2 - 4v - 8 \)  
1. Factor out the GCF, which is \( 4 \):
   \[ 4(v^2 - v - 2) \]
2. Find two numbers that multiply to \( -2 \) and add to \( -1 \). These numbers are \( -2 \) and \( 1 \).
3. The factorized form is:  
   \[ 4(v - 2)(v + 1) \]

Would you like further details on any of these solutions?

### Related Questions:
1. What methods can be used to factor quadratics when the leading coefficient is not 1?
2. How can you determine if a quadratic is prime (i.e., not factorable over the integers)?
3. What role does the discriminant play in factoring quadratics?
4. How do you apply the quadratic formula to solve quadratic equations?
5. How can completing the square help in factoring a quadratic?

### Tip:
Always start by looking for a greatest common factor (GCF) before attempting to factor the quadratic completely—it simplifies the expression and makes factoring easier.

Factor the following quadratic equations: b^2 - 6b + 8, n^2 + 6n + 8, 2n^2 + 6n - 108, 5n^2 + 10n + 20, 2k^2 + 22k + 60, a^2 - a - 90, p^2 + 11p + 10, 5v^2 - 30v + 40, 2p^2 + 2p - 4, 4v^2 - 4v - 8.

Learn how to factor quadratic equations such as b^2 - 6b + 8 and n^2 + 6n + 8 with step-by-step solutions. This page covers essential algebraic concepts like factoring, quadratic equations, and the zero-product property. Suitable for students in Grades 8-10.

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