Certainly! Let's factor the given expression step by step:
The given expression is:
[tex]\[ -18 + 42x \][/tex]
### Step 1: Identify the Greatest Common Factor (GCF)
First, we need to determine the greatest common factor (GCF) of the terms in the expression. The terms are [tex]\(-18\)[/tex] and [tex]\(42x\)[/tex].
- The factors of [tex]\(-18\)[/tex] are [tex]\(\pm 1, \pm 2, \pm 3, \pm 6, \pm 9, \pm 18\)[/tex].
- The factors of [tex]\(42\)[/tex] (ignoring [tex]\(x\)[/tex] for now) are [tex]\(\pm 1, \pm 2, \pm 3, \pm 6, \pm 7, \pm 14, \pm 21, \pm 42\)[/tex].
The highest common factor between [tex]\(-18\)[/tex] and [tex]\(42\)[/tex] is [tex]\(\pm 6\)[/tex]. In this case, we will factor out a positive 6.
### Step 2: Factor Out the GCF
Next, we write the expression as a product of the GCF and another expression.
[tex]\[ -18 + 42x = 6(\text{something}) \][/tex]
To find out what goes inside the parentheses, we divide each term by the GCF (6):
- For [tex]\(-18\)[/tex]: [tex]\(\frac{-18}{6} = -3\)[/tex]
- For [tex]\(42x\)[/tex]: [tex]\(\frac{42x}{6} = 7x\)[/tex]
Thus, we can write:
[tex]\[ -18 + 42x = 6(-3 + 7x) \][/tex]
### Step 3: Simplify the Expression Inside the Parentheses
Rearrange the terms in the parentheses for clarity:
[tex]\[ 6(-3 + 7x) = 6(7x - 3) \][/tex]
### Final Factored Form
The completely factored form of the expression [tex]\(-18 + 42x\)[/tex] is:
[tex]\[ 6(7x - 3) \][/tex]
This is the final answer.
