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:

For a quadratic equation, if \( (x - r) \) is a factor, substitute \( x = r \) into the equation and solve for the constant.

Answer 1

The Correct Option is C

Given that \( (x - 2) \) is a factor of \( px^2 - x - 6 \), we can use the factor theorem. According to the factor theorem, if \( (x - 2) \) is a factor, then substituting \( x = 2 \) into the equation should make the expression equal to zero. Substitute \( x = 2 \) into the equation \( px^2 - x - 6 \): \[ p(2)^2 - 2 - 6 = 0. \] This simplifies to: \[ 4p - 2 - 6 = 0 \quad \Rightarrow \quad 4p - 8 = 0 \quad \Rightarrow \quad 4p = 8 \quad \Rightarrow \quad p = 2. \] Thus, the value of \( p \) is \( \boxed{2} \).