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.

(x4 – y4) (x4 + x2y2 + y4), x2 – y2, x4 – y4.

Given: –


Polynomials p(x) = x4 – y4


And GCD[Greatest Common Divisor] = x2 – y2


And LCM[Lowest Common Multiple] = (x4 – y4)(x4 + x2y2 + y4)


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 = (x4 – y4) (x4 + x2y2 + y4) × (x2 – y2)


p(x) × q(x) = LCM × GCD


q(x) =


q(x) =


q(x) =


q(x) = (x4 + x2y2 + y4)(x2 – y2)


Conclusion: –


The other polynomial term q(x) is (x4 + x2y2 + y4)(x2 – y2)


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