Find the LCM of each pair of the following polynomials.

x⁴ + 3 x³ + 6 x² + 5x + 3, x⁴ + 2 x² + x + 2 whose GCD is x² + x + 1

Given: –

Polynomials x⁴ + 3 x³ + 6 x² + 5x + 3 , x⁴ + 2 x² + x + 2

And GCD[Greatest Common Divisor] = (x² + x + 1)

Formula used: –

The product of 2 polynomial is equal to product of their LCM

and GCD.

Product of 2 polynomial = LCM × GCD

Product of 2 polynomial = (x⁴ + 3x³ + 6x² + 5x + 3) × (x⁴ + 2x² + x + 2)

Product of 2 polynomial = LCM × GCD

LCM =

LCM =

LCM =

LCM = (x² + 2x + 3)(x⁴ + 2x² + x + 2)

Conclusion: –

The LCM of polynomial [x⁴ + 3 x³ + 6 x² + 5x + 3, x⁴ + 2 x² + x + 2] is

(x² + 2x + 3)(x⁴ + 2x² + x + 2)