Q. 2 E
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).
Answer :
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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