InterviewSolution
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InterviewSolution
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Let a `ne` 0 and P(x) be a polynomial of degree greater then 2.If P(x) leaves remianders a and a- when divided, respectively, by x + a and x - a, then find the remainder when P(x) is divided by `x^(2) - a^(2)`. |
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Answer» According to the question P(-a) = and P(a) = - a. Let the remainder, when P(x) is divided by `x^(2)-a^(2)` be Ax + B. Then `P(x) = Q (x) (x^(2)-a^(2))` + Ax + B, where Q (x) is the quotient Putting x = a, we get P(a) = 0 + Aa + B or Aa + B = - a ...(1) Putting x = - a, we get `-Aa + B = a` ...(2) Solving (1) and (2) , we get B = 0 and A = - 1 Hence, the requried remainder = Ax + B = - x |
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