Example 11 - Examine whether x + 2 is a factor of x3 + 3x2 - Check if factor

  1. Chapter 2 Class 9 Polynomials
  2. Serial order wise
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Example 11 Examine whether x + 2 is a factor of x3 + 3x2 + 5x + 6 and of 2x + 4. First checking whether x + 2 is a factor of x3 + 3x2 + 5x + 6 Finding remainder when x3 + 3x2 + 5x + 6 is divided by x + 2 Step 1: Put Divisor = 0 x + 2 = 0 x = – 2 Step 2: Let p(x) = x3 + 3x2 + 5x + 6 Putting x = – 2 p(–2) = (–2)3 + 3(–2)2 + 5(–2) + 6 = –8 + 12 – 10 + 6 = 0 Remainder = p(–2) = 0 Since remainder is zero x + 2 is a factor of x3 + 3x2 + 5x + 6 Checking whether x + 2 is a factor of 2x + 4 Finding remainder when 2x + 4 is divided by x + 2 Step 1: Put Divisor = 0 x + 2 = 0 x = – 2 Step 2: Let p(x) = 2x + 4 Putting x = – 2 p(–2) = 2(–2) + 4 = –4 + 4 = 0 Remainder = p(–2) = 0 Since remainder is zero x + 2 is a factor of 2x + 4

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