Find the other polynomial q(x) of each of the following, given that LCM and GCD and one polynomial p(x) respectively.

2(x + 1) (x² – 4), (x + 1), (x + 1) (x – 2).

Given: –

Polynomials p(x) = (x + 1)(x – 2)

And GCD[Greatest Common Divisor] = (x + 1)

And LCM[Lowest Common Multiple] = 2(x + 1) (x² – 4)

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 = 2(x + 1) (x² – 4) × (x + 1)

= 2(x + 1)² (x² – 2²)

= 2(x + 1)² (x – 2)(x + 2)

p(x) × q(x) = LCM × GCD

q(x) =

q(x) =

q(x) =

q(x) = 2(x + 2)(x + 1)

Conclusion: –

The other polynomial term q(x) is 2(x + 2)(x + 1)