Find the GCD of the following polynominals 3x4+6x3−12x2−24x and 4x4+x3+8x2−8x.
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Solution
Let f(x)=3x4+6x3−12x2−24x=3x(x3+2x2−4x−8). Let g(x)=4x4+14x3+8x2−8x=2x(2x3+7x2+4x−4) LetusfindtheGCDforthepolynomials x3+2x2−4x−8 and 2x3+7x2+4x−4 We choose the divisor to bex3+2x2−4x−8. Common factor of x3+2x2−4x−8 and2x3+7x2+4x−4 isx2+4x+4 Also common factor of 3x and 2x is x.Thus,GCD (f(x),g(x))=x(x2+4x+4).