Math, asked by lakshminivas8303, 6 months ago

The GCD of the polynomials f(x)=x^4-2x^3-x^2+4x-2 and x^2-6x+8​

Answers

Answered by kanmani17
0

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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