Find the LCM of each pair of the following polynomials.

x² – 5x + 6, x² + 4x – 12 whose GCD is x – 2.

Given: –

Polynomials x² – 5x + 6, x² + 4x – 12

And GCD[Greatest Common Divisor] = (x – 2)

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 = (x² – 5x + 6) × (x² + 4x – 12)

= ( x² – 2x – 3x + 6)(x² + 6x – 2x – 12)

= (x(x – 2) – 3(x – 2))(x(x + 6) – 2(x + 6))

= (x – 3)(x – 2)(x – 2)(x + 6)

Product of 2 polynomial = LCM × GCD

LCM =

LCM =

LCM = (x – 3)(x – 2)(x + 6)

Conclusion: –

The LCM of polynomial [x² – 5x + 6, x² + 4x – 12] is

(x – 3)(x – 2)(x + 6)