part b: factoring and solving quadratic functions without perfect squares trinomials (a=1) method). factor and solve the following quadratic functions binomials (hint: use x or diamond 5) ( x^2 + 3x + 2 ) factored form: solutions(s): 6) ( x^2 + 8x + 12 ) factored form: solutions(s): 7) ( x^2 + 5x + 4 ) factored form: solutions(s): 8) ( x^2 + 7x + 12 ) factored form: solutions(s):

Question

Accepted Answer

### Problem 5: $ x^2 + 3x + 2 $
# Explanation:
## Step 1: Factor the quadratic
We need two numbers that multiply to $ 2 $ and add to $ 3 $. The numbers are $ 1 $ and $ 2 $. So, the factored form is $ (x + 1)(x + 2) $.
## Step 2: Solve for $ x $
Set each factor equal to zero:
$ x + 1 = 0 $ gives $ x = -1 $
$ x + 2 = 0 $ gives $ x = -2 $
# Factored Form: $ (x + 1)(x + 2) $
# Solution(s): $ x = -1, x = -2 $

### Problem 6: $ x^2 + 8x + 12 $
# Explanation:
## Step 1: Factor the quadratic
We need two numbers that multiply to $ 12 $ and add to $ 8 $. The numbers are $ 2 $ and $ 6 $. So, the factored form is $ (x + 2)(x + 6) $.
## Step 2: Solve for $ x $
Set each factor equal to zero:
$ x + 2 = 0 $ gives $ x = -2 $
$ x + 6 = 0 $ gives $ x = -6 $
# Factored Form: $ (x + 2)(x + 6) $
# Solution(s): $ x = -2, x = -6 $

### Problem 7: $ x^2 + 5x + 4 $
# Explanation:
## Step 1: Factor the quadratic
We need two numbers that multiply to $ 4 $ and add to $ 5 $. The numbers are $ 1 $ and $ 4 $. So, the factored form is $ (x + 1)(x + 4) $.
## Step 2: Solve for $ x $
Set each factor equal to zero:
$ x + 1 = 0 $ gives $ x = -1 $
$ x + 4 = 0 $ gives $ x = -4 $
# Factored Form: $ (x + 1)(x + 4) $
# Solution(s): $ x = -1, x = -4 $

### Problem 8: $ x^2 + 7x + 12 $
# Explanation:
## Step 1: Factor the quadratic
We need two numbers that multiply to $ 12 $ and add to $ 7 $. The numbers are $ 3 $ and $ 4 $. So, the factored form is $ (x + 3)(x + 4) $.
## Step 2: Solve for $ x $
Set each factor equal to zero:
$ x + 3 = 0 $ gives $ x = -3 $
$ x + 4 = 0 $ gives $ x = -4 $
# Factored Form: $ (x + 3)(x + 4) $
# Solution(s): $ x = -3, x = -4 $

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QUESTION IMAGE

Question

Explanation:

Problem 5: \( x^2 + 3x + 2 \)

Step 1: Factor the quadratic

Step 2: Solve for \( x \)

Factored Form: \( (x + 1)(x + 2) \)

Solution(s): \( x = -1, x = -2 \)

Problem 6: \( x^2 + 8x + 12 \)

Step 1: Factor the quadratic

Step 2: Solve for \( x \)

Factored Form: \( (x + 2)(x + 6) \)

Solution(s): \( x = -2, x = -6 \)

Problem 7: \( x^2 + 5x + 4 \)

Step 1: Factor the quadratic

Step 2: Solve for \( x \)

Factored Form: \( (x + 1)(x + 4) \)

Solution(s): \( x = -1, x = -4 \)

Problem 8: \( x^2 + 7x + 12 \)

Answer:

Step 1: Factor the quadratic

Step 2: Solve for \( x \)

Factored Form: \( (x + 3)(x + 4) \)

Solution(s): \( x = -3, x = -4 \)