Question

If \( (x - 2) \) is a factor of \( px^2 - x - 6 \), then the value of \( p \) is:

• A. \( 2 \)
• B. \( 3 \)
• C. \( 1 \)
• D. \( 4 \)

Hint:

If \( (x - a) \) is a factor of \( f(x) \), then \( f(a) = 0 \).

Answer 1

The Correct Option is A

Since \( (x - 2) \) is a factor, substituting \( x = 2 \) should satisfy the equation:
\[ p(2)^2 - 2 - 6 = 0. \] \[ 4p - 2 - 6 = 0. \] \[ 4p = 8 \Rightarrow p = 2. \]