2026 · Q81
For the next two (02) items that follow:
x⁴ + px³ + qx² + x + 6 is divisible by x² − x − 6.
81. What is the value of p?
Elementary MathematicsAlgebra
- A−2
- B−1
- C1
- D2
Explanation
Since x²−x−6=(x−3)(x+2) divides the quartic, f(3)=0 gives 27p+9q=−90 and f(−2)=0 gives −8p+4q=−20, i.e. q=2p−5. Substituting: 3p+(2p−5)=−10, so 5p=−5 and p=−1, option B.