If (x - 5) notebooks cost Rs `( x^(2) - 13 x + 40)` then what is the cost of one notebook ?

Options

A. Rs. (x - 1)
B. Rs. (x - 2)
C. Rs. (x - 6)
D. Rs. (x - 8)

Answer

To find the cost of one notebook, we start with the information given in the problem:

1. We know that the cost of \( (x - 5) \) notebooks is given by the expression \( x^2 - 13x + 40 \).

2. To find the cost of one notebook, we need to divide the total cost by the number of notebooks. Therefore, we need to compute:

\[ \text{Cost of one notebook} = \frac{x^2 - 13x + 40}{x - 5} \]

3. Next, we will factor the quadratic expression \( x^2 - 13x + 40 \). We need to find two numbers that multiply to \( 40 \) (the constant term) and add up to \( -13 \) (the coefficient of \( x \)).

- The numbers that satisfy this condition are \( -8 \) and \( -5 \) because:
- \( -8 \times -5 = 40 \)
- \( -8 + (-5) = -13 \)

4. Therefore, we can factor the quadratic expression as follows:

\[ x^2 - 13x + 40 = (x - 8)(x - 5) \]

5. Now, substituting the factored form back into the equation for the cost of one notebook, we have:

\[ \text{Cost of one notebook} = \frac{(x - 8)(x - 5)}{x - 5} \]

6. Since \( x - 5 \) is in both the numerator and denominator, we can cancel it out (assuming \( x \neq 5 \)):

\[ \text{Cost of one notebook} = x - 8 \]

Thus, the cost of one notebook is \( x - 8 \).