The GCD of the polynomials f(x)=x^4-2x^3-x^2+4x-2 and x^2-6x+8
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Step-by-step explanation:
Find the GCD of the following polynomials.
x4 + 3x3 −x −3, x3 +x2 −5x + 3
Solution :
Let f(x) = x4 + 3x3 −x −3
g(x) = x3 +x2 −5x + 3
The degree of the polynomial f(x) is greater than g(x).
Note : If we have any missing term, we have to replace that place by 0.
The remainder is 3(x2 + 2x - 3), which is not equal to 0.So, we have to divide x3 +x2 −5x + 3 by x2 + 2x - 3 by leaving the remainder.
We get 0 as remainder by dividing the given polynomial by x2 + 2x - 3.
Hence the required GCD is x2 + 2x - 3.
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