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Factories x3 - 2x2 - x + 2 |
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Answer» Answer: Step-by-step EXPLANATION: LET take f(X) = x3 - 2x2 - x + 2 The constant term in f(x) is are �1 and� �2 Putting x = 1 in f(x), we have f(1) = (1)3 - 2(1)2 -1 + 2 = 1 - 2 - 1 + 2 = 0 According to REMAINDER theorem f(1) = 0 so that� (x - 1) is a factor of x3 - 2x2 - x + 2 Putting x = - 1 in f(x), we have f(-1) = (-1)3 - 2(-1)2 �(-1) + 2 = -1 - 2 + 1 + 2 = 0 According to remainder theorem f(-1) = 0 so that� (x + 1) is a factor of x3 - 2x2 - x + 2 Putting x =� 2 in f(x), we have f(2) = (2)3 - 2(2)2 �(2) + 2 = 8 -82 �- 2 + 2 = 0 According to remainder theorem f(2) = 0 so that� (x � 2 ) is a factor of x3 - 2x2 - x + 2 Here MAXIMUM power of x is 3 so that its can have maximum 3 factors So our answer is (x-1)(x+1)(x-2) |
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