Question

If \( (x + 3) \) is a factor of \( ax^2 + x + 1 \), then the value of \( a \) is:

• A. \( 3 \)
• B. \( \frac{9}{2} \)
• C. \( \frac{2}{9} \)
• D. \( 9 \)

Hint:

If \( (x + p) \) is a factor, substitute \( x = -p \) and solve for unknowns.

Answer 1

The Correct Option is B

Since \( (x + 3) \) is a factor, it must satisfy the equation:
\[ a(-3)^2 + (-3) + 1 = 0 \] \[ 9a - 3 + 1 = 0 \] \[ 9a - 2 = 0 \] \[ 9a = 2 \] \[ a = \frac{9}{2} \]