Q2 of 227 Page 92

Find the other polynomial q(x) of each of the following, given that LCM and GCD and one polynomial p(x) respectively.

(x – 1) (x – 2) (x2 – 3x + 3), (x – 1), (x3 – 4 x2 + 6x – 3).

Given: –


Polynomials p(x) = (x3 – 4 x2 + 6x – 3)


And GCD[Greatest Common Divisor] = (x – 1)


And LCM[Lowest Common Multiple] = (x – 1)(x – 2)(x2 – 3x + 3)


Formula used: –


The product of 2 polynomial is equal to product of their LCM


and GCD.


Product of 2 polynomial = LCM × GCD


p(x) × q(x) = LCM × GCD


LCM × GCD = (x – 1) (x – 2) (x2 – 3x + 3) × (x – 1)


= (x – 1)2 (x – 2) (x2 – 3x + 3)


p(x) × q(x) = LCM × GCD


q(x) =


q(x) =


q(x) =


q(x) =


q(x) = (x – 1)(x – 2)


Conclusion: –


The other polynomial term q(x) is (x – 1)(x – 2)


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