Question

2. Find the LCM of each pair of the following polynomials (i) \( a^{2}+4 a-12, a^{2}-5 a+6 \) whose \( G C D \) is \( a-2 \) (ii) \( x^{4}-27 a^{3} x,(x-3 a)^{2} \) whose GCD is \( (x-3 a) \)

Answer 1

(i)

p(x) = a² + 4a - 12

= a² + 6a - 2a - 12

= a (a + 6) - 2(a + 6)

= (a + 6) (a - 2)

g(x) = a² - 5a + 6

= a² - 3a - 2a + 6

(ii)