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).

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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