Advertisements
Advertisements
Question
Find the LCM pair of the following polynomials
a2 + 4a – 12, a2 – 5a + 6 whose GCD is a – 2
Advertisements
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)
APPEARS IN
RELATED QUESTIONS
Find the G.C.D. of the given polynomials
x4 + 3x3 – x – 3, x3 + x2 – 5x + 3
Find the G.C.D. of the given polynomials
x4 – 1, x3 – 11x2 + x – 11
Find the L.C.M. of the given expressions
4x2y, 8x3y2
Find the L.C.M. of the given expressions
16m, – 12m2n2, 8n2
Find the LCM and GCD for the following and verify that f(x) × g(x) = LCM × GCD
(x3 – 1) (x + 1), (x3 + 1)
Find the LCM and GCD for the following and verify that f(x) × g(x) = LCM × GCD
(x2y + xy2), (x2 + xy)
Find the LCM pair of the following polynomials
x4 – 27a3x, (x – 3a)2 whose GCD is (x – 3a)
Find the GCD pair of the following polynomials
12(x4 – x3), 8(x4 – 3x3 + 2x2) whose LCM is 24x3 (x – 1)(x – 2)
Find the GCD pair of the following polynomials
(x3 + y3), (x4 + x2y2 + y4) whose LCM is (x3 + y3) (x2 + xy + y2)
Find the least common multiple of xy(k2 + 1) + k(x2 + y2) and xy(k2 – 1) + k(x2 – y2)
