The expression to be added to `(5x^(2) - 7x + 2)` to produce `(7x^(2) -1)` is:

Options

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

Answer

To find the expression that needs to be added to \(5x^2 - 7x + 2\) to produce \(7x^2 - 1\), we can set up the equation:

\[ (5x^2 - 7x + 2) + P = 7x^2 - 1 \]

Where \(P\) is the expression we want to find.

### Step 1: Rearranging the equation
We can rearrange the equation to solve for \(P\):

\[ P = (7x^2 - 1) - (5x^2 - 7x + 2) \]

### Step 2: Distributing the negative sign
Now we will distribute the negative sign across the expression in parentheses:

\[ P = 7x^2 - 1 - 5x^2 + 7x - 2 \]

### Step 3: Combining like terms
Next, we will combine the like terms:

- For \(x^2\) terms: \(7x^2 - 5x^2 = 2x^2\)
- For \(x\) terms: \(7x\) (there are no other \(x\) terms to combine)
- For constant terms: \(-1 - 2 = -3\)

Putting it all together, we have:

\[ P = 2x^2 + 7x - 3 \]

### Final Result
Thus, the expression that needs to be added is:

\[ \boxed{2x^2 + 7x - 3} \]

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