Factor the following expressions.
`x^(2)+3x-18`

Answer

To factor the quadratic expression \( x^2 + 3x - 18 \), we will follow these steps:

### Step 1: Identify the coefficients
The given expression is in the standard form of a quadratic equation \( ax^2 + bx + c \), where:
- \( a = 1 \)
- \( b = 3 \)
- \( c = -18 \)

### Step 2: Find two numbers that multiply to \( ac \) and add to \( b \)
We need to find two numbers that multiply to \( ac = 1 \times -18 = -18 \) and add up to \( b = 3 \).

After checking the pairs of factors of -18, we find:
- \( 6 \) and \( -3 \) satisfy the conditions because:
- \( 6 \times (-3) = -18 \)
- \( 6 + (-3) = 3 \)

### Step 3: Rewrite the middle term using the two numbers
We can rewrite the expression \( x^2 + 3x - 18 \) as:
\[ x^2 + 6x - 3x - 18 \]

### Step 4: Group the terms
Next, we group the terms:
\[ (x^2 + 6x) + (-3x - 18) \]

### Step 5: Factor by grouping
Now, we factor out the common terms from each group:
1. From the first group \( (x^2 + 6x) \), we can factor out \( x \):
\[ x(x + 6) \]
2. From the second group \( (-3x - 18) \), we can factor out \( -3 \):
\[ -3(x + 6) \]

Now we have:
\[ x(x + 6) - 3(x + 6) \]

### Step 6: Factor out the common binomial factor
We can see that \( (x + 6) \) is a common factor:
\[ (x + 6)(x - 3) \]

### Step 7: Write the final factored form
Thus, the factored form of the expression \( x^2 + 3x - 18 \) is:
\[ (x + 6)(x - 3) \]

### Summary of the solution:
The expression \( x^2 + 3x - 18 \) factors to \( (x + 6)(x - 3) \).

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