The expression to be added to `(7x^(2) - x + 9)` to produce `(5x^(2) - 4)` is

Options

A. `-2x^(2) + x - 13`
B. `2x^(2) + 3`
C. `2x^(2) - 3`
D. `2x^(2) + 7x`

Answer

To find the expression that needs to be added to \( (7x^2 - x + 9) \) to produce \( (5x^2 - 4) \), we can follow these steps:

### Step 1: Set up the equation
Let the expression we need to find be \( A \). We can set up the equation:
\[ (7x^2 - x + 9) + A = (5x^2 - 4) \]

### Step 2: Isolate \( A \)
To find \( A \), we can rearrange the equation:
\[ A = (5x^2 - 4) - (7x^2 - x + 9) \]

### Step 3: Distribute the negative sign
Now, distribute the negative sign across the second expression:
\[ A = (5x^2 - 4) - 7x^2 + x - 9 \]

### Step 4: Combine like terms
Now, combine the like terms:
1. For \( x^2 \) terms: \( 5x^2 - 7x^2 = -2x^2 \)
2. For \( x \) terms: \( 0 + x = x \)
3. For constant terms: \( -4 - 9 = -13 \)

Putting it all together:
\[ A = -2x^2 + x - 13 \]

### Final Answer
Thus, the expression that needs to be added is:
\[ A = -2x^2 + x - 13 \]

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