Multiply `x^(2) - 4x + 7` by x - 2.

Answer

To multiply the expression \( x^2 - 4x + 7 \) by \( x - 2 \), we will use the distributive property (also known as the FOIL method for binomials). Here are the steps:

### Step 1: Distribute \( x \) to each term in the first expression
Multiply \( x \) by each term in \( x^2 - 4x + 7 \):
\[ x \cdot (x^2 - 4x + 7) = x^3 - 4x^2 + 7x \]

### Step 2: Distribute \( -2 \) to each term in the first expression
Now, multiply \( -2 \) by each term in \( x^2 - 4x + 7 \):
\[ -2 \cdot (x^2 - 4x + 7) = -2x^2 + 8x - 14 \]

### Step 3: Combine the results from Step 1 and Step 2
Now, we will add the results from Step 1 and Step 2 together:
\[ x^3 - 4x^2 + 7x - 2x^2 + 8x - 14 \]

### Step 4: Combine like terms
Now, we combine the like terms:
- The \( x^2 \) terms: \( -4x^2 - 2x^2 = -6x^2 \)
- The \( x \) terms: \( 7x + 8x = 15x \)

Putting it all together, we get:
\[ x^3 - 6x^2 + 15x - 14 \]

### Final Answer
The final result of multiplying \( x^2 - 4x + 7 \) by \( x - 2 \) is:
\[ \boxed{x^3 - 6x^2 + 15x - 14} \]

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