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Polynomials — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsPolynomials1 Mark
MCQ
When p(x) = x3 + ax2 + 2x + a is divided by x + a, the remainder is:
  • A
    1
  • B
    0
  • C
    a
  • D
    -a
✓

Answer

  1. -a
    Solution:
    x + a = 0
    ⇒ x = -a
    By the remainder theorem, we know that when p(x) is divided by (x + a), the remainder is p (-a).
    Thus, we have: P(-a) = (-a)3 + a × (-a)2 + 2 × (-a) + a
    = -a3 + a3 - 2a + a
    = -a

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