Question

If \( x^4 - x^3 + 2x^2 + ax + b \) is exactly divisible by \( x^2 - 3x + 2 \), then \( (a, b) \) is

• A. \( (14, -12) \)
• B. \( (-14, 12) \)
• C. \( (14, 12) \)
• D. \( (-14, -12) \)

Hint:

When dividing polynomials, ensure the remainder is zero to confirm divisibility.

Answer 1

The Correct Option is B

To find the values of \( a \) and \( b \), we perform polynomial division on \( \frac{x^4 - x^3 + 2x^2 + ax + b}{x^2 - 3x + 2} \). After dividing, we get the quotient and the remainder. For the polynomial to be exactly divisible, the remainder must be zero. Solving the equations for the coefficients of the remainder will yield \( a = -14 \) and \( b = 12 \).