Answered

Question 1 of 10

Match each value to the correct location in the expression. Each value can be used more than once, but not all values will be used.

Factor the quadratic expression given below completely.

[tex]\[ 4x^2 + 8x - 60 \][/tex]

Fill in the following expression completely.

[tex]\[ (x + \cdots)(4x - 3) \][/tex]

Possible values:

[tex]\[ 4, \quad 1, \quad 8, \quad 5, \quad x \][/tex]

Submit



Answer :

GinnyAnswer
Let's work through the given quadratic expression step-by-step as if factorizing it manually:

Given quadratic expression:
[tex]\[ 4x^2 + 8x - 60 \][/tex]

### Step 1: Identify the coefficients
- The coefficient of [tex]\(x^2\)[/tex] is 4.
- The coefficient of [tex]\(x\)[/tex] is 8.
- The constant term is -60.

### Step 2: Find two numbers that multiply to [tex]\((4 -60) = -240\)[/tex] and add to 8
- The numbers are 20 and -12 because [tex]\(20 (-12) = -240\)[/tex] and [tex]\(20 + (-12) = 8\)[/tex].

### Step 3: Rewrite the middle term (8x) using 20x and -12x
[tex]\[ 4x^2 + 8x - 60 = 4x^2 + 20x - 12x - 60 \][/tex]

### Step 4: Group the terms
[tex]\[ 4x^2 + 20x - 12x - 60 \][/tex]
Group the first two terms and the last two terms:
[tex]\[ = (4x^2 + 20x) + (-12x - 60) \][/tex]

### Step 5: Factor out the greatest common factor (GCF) from each group
From [tex]\(4x^2 + 20x\)[/tex], factor out [tex]\(4x\)[/tex]:
[tex]\[ = 4x(x + 5) \][/tex]
From [tex]\(-12x - 60\)[/tex], factor out [tex]\(-12\)[/tex]:
[tex]\[ = -12(x + 5) \][/tex]

### Step 6: Factor out the common binomial factor [tex]\((x + 5)\)[/tex]
[tex]\[ 4x(x + 5) - 12(x + 5) = (4x - 12)(x + 5) \][/tex]

### Step 7: Simplify the coefficients
[tex]\[ (4x - 12)(x + 5) = 4(x - 3)(x + 5) \][/tex]

Thus, the completely factorized form of the given quadratic expression [tex]\(4x^2 + 8x - 60\)[/tex] is:
[tex]\[ 4(x - 3)(x + 5) \][/tex]

So, the final filled expression is:
[tex]\[ \left(4 \left( x - 3 \right) \left( x + 5 \right) \right) \][/tex]

Other Questions