find the gcm and lcm of polynomials x² - 5x + 6 and x² - 4
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Answer:
Given:
f(x)=x
2
−4
g(x)=x
2
+5x+6
L.C.M = (x−2)
2
Factor of x
2
+5x+6=(x+2)(x+3)
Factor of x
2
−4=(x+2)(x−2)
Using the formula,
f(x)×g(x)=H.C.F×L.C.M
H.C.F =
(x−2)
2
(x+2)(x+3)(x+2)(x−2)
H.C.F =
x−2
(x+2)
2
(x+3)
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