Find the G.C.D. and L.C.M. of the following polynomials: p(x) = 6(x - 2)(x2 + x - 6) and, q(x) = 3(x2 + 4x - 12).
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P(x) = 6(x -2)( x² + x - 6)
P(x ) = 6(x -2)(x² +3x -2x - 6)
P(x) = 6(x -2)(x-2)(x +3)
P( x ) = 3 × 2 (x -2)²(x +3)
again,
g(x) = 3(x² + 4x -12)
g(x) = 3(x² + 6x -2x -12)
g(x) = 3(x + 6)(x -2)
GCD { P(x), g(x) } = highest common factors = 3(x -2)
LCM {P(x) , g(x) } = 6(x -2)²(x +3)(x + 6)
P(x ) = 6(x -2)(x² +3x -2x - 6)
P(x) = 6(x -2)(x-2)(x +3)
P( x ) = 3 × 2 (x -2)²(x +3)
again,
g(x) = 3(x² + 4x -12)
g(x) = 3(x² + 6x -2x -12)
g(x) = 3(x + 6)(x -2)
GCD { P(x), g(x) } = highest common factors = 3(x -2)
LCM {P(x) , g(x) } = 6(x -2)²(x +3)(x + 6)
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