If `A = 19x^(2) - x + 6, B = x^(2) - x, C = 4x - 1`, find A-B+C.

Options

A. `17x^(2) - 5x + 7`
B. ` 18x^(2) + 4x -5`
C. `24x^(2) - 4x +7`
D. `18x^(2) +4x +5`

Answer

To solve the expression \( A - B + C \) where \( A = 19x^2 - x + 6 \), \( B = x^2 - x \), and \( C = 4x - 1 \), we will follow these steps:

### Step 1: Write down the expressions for A, B, and C
We have:
- \( A = 19x^2 - x + 6 \)
- \( B = x^2 - x \)
- \( C = 4x - 1 \)

### Step 2: Substitute the expressions into \( A - B + C \)
Now, we substitute the values of A, B, and C into the expression:
\[ A - B + C = (19x^2 - x + 6) - (x^2 - x) + (4x - 1) \]

### Step 3: Distribute the negative sign in front of B
When we subtract B, we need to distribute the negative sign:
\[ = 19x^2 - x + 6 - x^2 + x + 4x - 1 \]

### Step 4: Combine like terms
Now, we will combine the like terms:
- For \( x^2 \) terms: \( 19x^2 - x^2 = 18x^2 \)
- For \( x \) terms: \( -x + x + 4x = 4x \)
- For constant terms: \( 6 - 1 = 5 \)

Putting it all together, we have:
\[ A - B + C = 18x^2 + 4x + 5 \]

### Final Answer
Thus, the final expression is:
\[ \boxed{18x^2 + 4x + 5} \]

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