Find the GCD of
36(3x^4+5x^3-2x^2) and 54(27x^4-x)
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14
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SOLUTION:
36(3x⁴+5x³-2x²)
f(x)=36x²(3x²+5x-2)
=36x²[3x²+(6-1)x-2)
=36x²(3x²+6x-x-2)
=36x²[3x(x+2)-1(x+2)]
=36x²(x+2)(3x-1)
=2x2x3x3x²(x+2)(3x-1)
g(x)=54(27x⁴-x)
=54x(27x³-1)
=54x(3x³-1³)
=54x(3x-1)[(3x)²+3x.1-1²)]
=54x(3x-1)(3x²+3x-1)
=2x3x3x3x(3x-1)(3x²+3x-1)
GCD=18x²(3x-1)
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