If `x=49`, then `x^(3) - 5x^(2) - 2x - 6=?`

Options

A. 53040
B. 93990
C. 1,05,540
D. 1,16,040

Answer

To solve the expression \( x^3 - 5x^2 - 2x - 6 \) for \( x = 49 \), we will follow these steps:

### Step 1: Substitute the value of \( x \)
We start by substituting \( x = 49 \) into the expression.

\[ 49^3 - 5 \cdot 49^2 - 2 \cdot 49 - 6 \]

### Step 2: Calculate \( 49^3 \)
Now, we calculate \( 49^3 \).

\[ 49^3 = 49 \times 49 \times 49 \]
First, calculate \( 49 \times 49 \):

\[ 49 \times 49 = 2401 \]

Now multiply by 49 again:

\[ 2401 \times 49 = 117649 \]

So, \( 49^3 = 117649 \).

### Step 3: Calculate \( 5 \cdot 49^2 \)
Next, we calculate \( 5 \cdot 49^2 \).

\[ 49^2 = 2401 \quad \text{(from previous calculation)} \]
Now multiply by 5:

\[ 5 \cdot 2401 = 12005 \]

### Step 4: Calculate \( 2 \cdot 49 \)
Now we calculate \( 2 \cdot 49 \):

\[ 2 \cdot 49 = 98 \]

### Step 5: Combine all the calculated values
Now we can substitute all the calculated values back into the expression:

\[ 117649 - 12005 - 98 - 6 \]

### Step 6: Perform the subtraction
Now, we will perform the subtraction step-by-step:

1. First, subtract \( 12005 \) from \( 117649 \):

\[ 117649 - 12005 = 105644 \]

2. Next, subtract \( 98 \):

\[ 105644 - 98 = 105546 \]

3. Finally, subtract \( 6 \):

\[ 105546 - 6 = 105540 \]

### Final Answer
Thus, the value of \( x^3 - 5x^2 - 2x - 6 \) when \( x = 49 \) is:

\[ \boxed{105540} \]