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Class 10 Textbook 2017 : Biology (Madhav International School, Ahmedabad)

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Jenil Makadiya
Madhav International School, Ahmedabad
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Question Bank Factor Theorem 1. 2. Without performing the actual division process, find the remainder, when 3x3 + 5x2 11x 4 is divided by 3x + 1 Solution. Let f(x) = 3x3 + 5x2 11x 4. 1 1 Since, 3x + 1 = 3 x + = 3 x 3 3 By remainder theorem, the required remainder 1 = f 3 3 2 1 1 1 = 3. + 5. 11. 4 3 3 3 1 11 1 + 5. + 4 = 3. 27 9 3 1 5 11 1 + 5 + 33 36 1 + + 4= = = 9 9 3 9 9 Find the values of the constants a and b, if (x 2) and (x + 3) are both factors of the expression (x3 + ax2 + bx 12). Solution. Let p(x) = x3 + ax2 + bx 12 Now, (x 2) is a factor of p(x) p(2) = 0 [23 + a 22 + b 2 12] = 0 4a + 2b = 4 2a + b = 2 ... (i) Again, (x + 3) is a factor of p(x) p ( 3) = 0 [( 3)3 + a ( 3)2 + b ( 3) 12] = 0 9a 3b = 39 3a b = 13 ... (ii) On adding (i) and (ii), we get 5a = 15 a = 3 Substituting a = 3 in (i), we get 2 3 + b = 2 b = (2 6) = 4 Hence, a = 3 and b = 4. Math Class X 1 Question Bank

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