factor each completely.
1) $n^2 + 12n + 35$
2) $x^2 - 3x - 40$
3) $p^2 + p - 72$
4) $n^2 + 12n + 35$
5) $m^2 - 8m - 20$
6) $v^2 - 2v + 1$
7) $k^2 + 4k - 60$
8) $k^2 - 15k + 56$
9) $x^2 - x - 72$
10) $n^2 + 15n + 56$

Question

Accepted Answer

### Problem 1: $ n^2 + 12n + 35 $
# Explanation:
## Step1: Find two numbers that multiply to 35 and add to 12.
The numbers are 5 and 7 (since $ 5 \times 7 = 35 $ and $ 5 + 7 = 12 $).
## Step2: Factor the quadratic.
Using the numbers from Step 1, we can write the quadratic as $ (n + 5)(n + 7) $.
# Answer: $ (n + 5)(n + 7) $

### Problem 2: $ x^2 - 3x - 40 $
# Explanation:
## Step1: Find two numbers that multiply to -40 and add to -3.
The numbers are -8 and 5 (since $ -8 \times 5 = -40 $ and $ -8 + 5 = -3 $).
## Step2: Factor the quadratic.
Using the numbers from Step 1, we can write the quadratic as $ (x - 8)(x + 5) $.
# Answer: $ (x - 8)(x + 5) $

### Problem 3: $ p^2 + p - 72 $
# Explanation:
## Step1: Find two numbers that multiply to -72 and add to 1.
The numbers are 9 and -8 (since $ 9 \times (-8) = -72 $ and $ 9 + (-8) = 1 $).
## Step2: Factor the quadratic.
Using the numbers from Step 1, we can write the quadratic as $ (p + 9)(p - 8) $.
# Answer: $ (p + 9)(p - 8) $

### Problem 4: $ n^2 + 12n + 35 $
# Explanation:
## Step1: Find two numbers that multiply to 35 and add to 12.
The numbers are 5 and 7 (since $ 5 \times 7 = 35 $ and $ 5 + 7 = 12 $).
## Step2: Factor the quadratic.
Using the numbers from Step 1, we can write the quadratic as $ (n + 5)(n + 7) $.
# Answer: $ (n + 5)(n + 7) $

### Problem 5: $ m^2 - 8m - 20 $
# Explanation:
## Step1: Find two numbers that multiply to -20 and add to -8.
The numbers are -10 and 2 (since $ -10 \times 2 = -20 $ and $ -10 + 2 = -8 $).
## Step2: Factor the quadratic.
Using the numbers from Step 1, we can write the quadratic as $ (m - 10)(m + 2) $.
# Answer: $ (m - 10)(m + 2) $

### Problem 6: $ v^2 - 2v + 1 $
# Explanation:
## Step1: Recognize this as a perfect square trinomial.
The quadratic can be written as $ (v - 1)^2 $ because $ (v - 1)^2 = v^2 - 2v + 1 $.
# Answer: $ (v - 1)^2 $

### Problem 7: $ k^2 + 4k - 60 $
# Explanation:
## Step1: Find two numbers that multiply to -60 and add to 4.
The numbers are 10 and -6 (since $ 10 \times (-6) = -60 $ and $ 10 + (-6) = 4 $).
## Step2: Factor the quadratic.
Using the numbers from Step 1, we can write the quadratic as $ (k + 10)(k - 6) $.
# Answer: $ (k + 10)(k - 6) $

### Problem 8: $ k^2 - 15k + 56 $
# Explanation:
## Step1: Find two numbers that multiply to 56 and add to -15.
The numbers are -7 and -8 (since $ (-7) \times (-8) = 56 $ and $ -7 + (-8) = -15 $).
## Step2: Factor the quadratic.
Using the numbers from Step 1, we can write the quadratic as $ (k - 7)(k - 8) $.
# Answer: $ (k - 7)(k - 8) $

### Problem 9: $ x^2 - x - 72 $
# Explanation:
## Step1: Find two numbers that multiply to -72 and add to -1.
The numbers are -9 and 8 (since $ -9 \times 8 = -72 $ and $ -9 + 8 = -1 $).
## Step2: Factor the quadratic.
Using the numbers from Step 1, we can write the quadratic as $ (x - 9)(x + 8) $.
# Answer: $ (x - 9)(x + 8) $

### Problem 10: $ n^2 + 15n + 56 $
# Explanation:
## Step1: Find two numbers that multiply to 56 and add to 15.
The numbers are 7 and 8 (since $ 7 \times 8 = 56 $ and $ 7 + 8 = 15 $).
## Step2: Factor the quadratic.
Using the numbers from Step 1, we can write the quadratic as $ (n + 7)(n + 8) $.
# Answer: $ (n + 7)(n + 8) $

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QUESTION IMAGE

Question

Explanation:

Problem 1: \( n^2 + 12n + 35 \)

Step1: Find two numbers that multiply to 35 and add to 12.

Step2: Factor the quadratic.

Step1: Find two numbers that multiply to -40 and add to -3.

Step2: Factor the quadratic.

Step1: Find two numbers that multiply to -72 and add to 1.

Step2: Factor the quadratic.

Answer:

Problem 2: \( x^2 - 3x - 40 \)