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.

(4x + 5)3 (3x – 7)3, (4x + 5) (3x – 7)2, (4x + 5)3 (3x – 7)2

Given: –


Polynomials p(x) = (4x + 5)3 (3x – 7)2


And GCD[Greatest Common Divisor] = (4x + 5) (3x – 7)2


And LCM[Lowest Common Multiple] = (4x + 5)3 (3x – 7)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 = (4x + 5)3 × (3x – 7)3 × (4x + 5) × (3x – 7)2


= (4x + 5)4(3x – 7)5


p(x) × q(x) = LCM × GCD


q(x) =


q(x) =


q(x) =


q(x) = (4x + 5)(3x – 7)3


Conclusion: –


The other polynomial term q(x) is (4x + 5)(3x – 7)3


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