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Applied Mathematical Methods by Bhaskar Dasgupta

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Chapter 19

1 Note that the new equations are not independent, they are merely linearly independent, as they are generated by multiplication with x, the variable or the unknown.

2 The degree of a multivariate polynomial equation is given by the largest total degree of the variables, among the terms of the polynomial.

3 Note the factors at this stage carefully. They involve x, hence the resulting equation is linearly independent. Further, by virtue of their special structure, they eliminate higher powers of x.

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