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Ex 2.3, 4 - On dividing x3 - 3x2 + x + 2 by polynomial g(x) - Division algorithm

  1. Chapter 2 Class 10 Polynomials
  2. Serial order wise
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Ex2.3, 4 On dividing x3 – 3x2 + x + 2 by a polynomial g(x), the quotient and remainder were x − 2 and − 2x + 4, respectively. Find g(x). Introduction Dividend = Divisor × Quotient + Remainder 7 = 3 × 2 + 1 Ex2.3, 4 On dividing x3 – 3x2 + x + 2 by a polynomial g(x), the quotient and remainder were x − 2 and − 2x + 4, respectively. Find g(x). We know that Dividend = Divisor × Quotient + Remainder Here, Dividend = x3 – 3x2 + x + 2 Divisor = g(x) Quotient = (x − 2) Remainder = (− 2x + 4) Putting values in (1) x3 – 3x2 + x + 2 = g(x) × (x – 2) + (-2x + 4) x3 – 3x2 + x + 2 + 2x – 4 = g(x) (x – 2) x3 – 3x2 + 3x – 2 = g(x) (x – 2) g(x) = (𝑥3 −3𝑥2 + 3𝑥 − 2)/(𝑥 −2) Therefore, g(x) = Quotient = x2 – x + 1

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