The degree of the polynomial $(x + 1) (x^{2} - x - x^{4} + 1)$ is:

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Solution

The correct option is B 5
The degree of a polynomial is the highest degree of its monomials (individual terms) with non-zero coefficients. The degree of a term is the sum of the exponents of the variables that appear in it, and thus is a non-negative integer.

Here, given polynomial $= (x + 1) (x^{2} - x - x^{4} + 1)$
$= x^{3} + x^{2} - x^{2} - x - x^{5} - x^{4} + x + 1$
$= x^{3} - x^{5} - x^{4} + 1$
The highest degree of individual terms $= 5$
So, $D$ is correct.

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