Q23 of 108 Page 46

The LCM of two polynomials in x3 – 6x2 + 3x + 10 and HCF is (x + 1). If one polynomial is x2 – 4x – 5 then find the other polynomial.

LCM = x3 – 6x2 + 3x + 10

= x3 – 5x2 - x2 + 3x + 10


= x2(x – 5) – (x2 – 3x – 10)


= x2(x – 5) – (x2 – 5x + 2x – 10)


= x2(x – 5) – (x(x – 5) + 2(x – 5))


= x2(x – 5) – (x + 2) (x – 5)


= (x – 5) [x2 – x -2]


= (x – 5) [x2 – 2x + x -2]


= (x – 5) [x(x – 2) +1(x – 2)]


= (x – 5) (x – 2) (x + 1)


Since HCF = (x + 1) it belongs to both the polynomials.


So u(x) = (x + 1) (x – 5)


= x2 – 4x - 5


So v(x) = (x + 1) (x – 2)


= x2 – x - 2


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