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Find the value of k, if x-3 is a factor of 5x^3-2x^2+x+k.(a) 50(b) 60(c) -60(d) -120This question was addressed to me at a job interview.The question is from Factorisation of Polynomials and Algebraic Identities in portion Polynomials of Mathematics – Class 9

Answer»

The CORRECT option is (d) -120

The explanation is: According to factor theorem, x-a is a factor of P(x) if p(a) = 0.

Here, it is GIVEN that x-3 is a factor of 5x^3-2x^2+x+k.

Therefore, p(3) must be EQUAL to zero.

p(3) = 5(3)^3-2(3)^2+3+k = 0

Therefore, 5(27) – 2(9) + 3 + k = 0

135 – 18 + 3 + k=0

120 + k = 0

Therefore,k= -120



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