Coefficient of `x^(2)" in "(x^(2)-1) (x-2)` is

Options

A. 2
B. `-2`
C. `-1`
D. `+1`

Answer

To find the coefficient of \( x^2 \) in the expression \( (x^2 - 1)(x - 2) \), we will follow these steps:

### Step 1: Expand the expression
We need to multiply the two polynomials \( (x^2 - 1) \) and \( (x - 2) \).

\[ (x^2 - 1)(x - 2) = x^2 \cdot (x - 2) - 1 \cdot (x - 2) \]

### Step 2: Distribute \( x^2 \) and \(-1\)
Now we will distribute \( x^2 \) and \(-1\) across \( (x - 2) \):

1. Multiply \( x^2 \) by \( x \):
\[ x^2 \cdot x = x^3 \]

2. Multiply \( x^2 \) by \(-2\):
\[ x^2 \cdot (-2) = -2x^2 \]

3. Multiply \(-1\) by \( x \):
\[ -1 \cdot x = -x \]

4. Multiply \(-1\) by \(-2\):
\[ -1 \cdot (-2) = 2 \]

### Step 3: Combine all the terms
Now we combine all the terms we obtained from the distribution:

\[ x^3 - 2x^2 - x + 2 \]

### Step 4: Identify the coefficient of \( x^2 \)
From the expanded expression \( x^3 - 2x^2 - x + 2 \), we can identify the coefficient of \( x^2 \):

The coefficient of \( x^2 \) is \(-2\).

### Final Answer
Thus, the coefficient of \( x^2 \) in the expression \( (x^2 - 1)(x - 2) \) is \(-2\).

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