QQuestion
What must be added to x³ + 7x² + 3x + 2 so that the resulting polynomial is exactly divisible by x + 2?
(a) −40
(b) −16
(c) 16
(d) 40
ICSEClass XMathematicsFactorisation01 Mark2026 Moderate
✓Answer
(b) −16
Explanation:
Let P(x) = x³ + 7x² + 3x + 2.
By the Remainder Theorem, the remainder when P(x) is divided by x + 2 is P(−2).
P(−2) = (−2)³ + 7(−2)² + 3(−2) + 2
⇒ P(−2) = −8 + 28 − 6 + 2
⇒ P(−2) = 16
Therefore, −16 must be added to make the remainder zero.
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