What is the coefficient and index form for the polynomial $x^{6} - 3 x^{4} + x^{3} - 2 x^{2} + 10$ ?

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Solution

The numerical values of the terms in a polynomial are called coefficients of the polynomial.
So, Coefficient for the polynomial $x^{6} - 3 x^{4} + x^{3} - 2 x^{2} + 10$ is $(1, 0, - 3, 1, - 2, 0)$
Index form $=$ $x^{6} + 0 x^{5} - 3 x^{4} + x^{3} - 2 x^{2} + 0 x + 10$

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