Find the other polynomial q(x) of each of the following, given that LCM and GCD and one polynomial p(x) respectively.
(x + 1)2 (x + 2)2, (x + 1) (x + 2), (x + 1)2 (x + 2)
Given: –
Polynomials p(x) = (x + 1)2 (x + 2)
And GCD[Greatest Common Divisor] = (x + 1) (x + 2)
And LCM[Lowest Common Multiple] = (x + 1)2 (x + 2)2
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)2 × (x + 2)2 × (x + 1) × (x + 2)
p(x) × q(x) = LCM × GCD
q(x) = 
q(x) = 
q(x) = 
q(x) = (x + 1)(x + 2)2
Conclusion: –
The other polynomial term q(x) is (x + 1)(x + 2)2
Couldn't generate an explanation.
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