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Question
Find the LCM pair of the following polynomials
a2 + 4a – 12, a2 – 5a + 6 whose GCD is a – 2
Solution
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
= a(a – 3) – 2 (a – 3)
= (a – 3) (a – 2)
L.C.M. = `("p"(x) xx "g"(x))/("G"."C"."D".)`
= `(("a" + 6)("a" - 2) xx ("a" - 3)("a" - 2))/(("a" - 2))`
= (a + 6) (a – 3) (a – 2)
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