

InterviewSolution
1. |
Show that,(i) x + 3 is a factor of 69 + 11c – x2 + x3(ii) 2x – 3 is a factor of x + 2x3 -9x2 +12 |
Answer» (i) According to the question, Let p(x) = 69 + 11x − x2 + x3 and g(x) = x + 3 g(x) = x + 3 zero of g(x) ⇒ g(x) = 0 x + 3 = 0 x = – 3 Therefore, zero of g(x) = – 3 So, substituting the value of x in p(x), we get, p( – 3) = 69 + 11( – 3) –( – 3)2 + ( – 3)3 = 69 – 69 = 0 Since, the remainder = zero, We can say that, g(x) = x + 3 is factor of p(x) = 69 + 11x − x2 + x3 (ii) According to the question, Let p(x) = x + 2x3 – 9x2 + 12 and g(x) =2x−3 g(x) = 2x – 3 zero of g(x) ⇒ g(x) = 0 2x – 3 = 0 x = 3/2 Therefore, zero of g(x) = 3/2 So, substituting the value of x in p(x), we get, P(3/2) = 3/2 + 2(3/2)3 – 9(3/2)2 + 12 = (81 – 81) / 4 = 0 Since, the remainder = zero, We can say that, g(x) = 2x – 3 is factor of p(x) = x + 2x3 – 9x2 + 12 |
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