Write the degree of the following polynomial:
$2 x^{3} + 5 x^{2} - 3 x + 1$

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Solution

Degree of the polynomial:
The highest power(exponent) of variable of all terms that appear with non-zero coefficients in a polynomial is called the degree of the polynomial.
Here, the highest power of $x$ is $3$ .
Hence, the degree of the given polynomial is $3$ .

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\lim_{x \to 1} \frac{x^{4} - 3 x^{3} + 2}{x^{3} - 5 x^{2} + 3 x + 1}

Write the degree of the following polynomial :

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Which of the following expressions are polynomials? In case of a polynomial, write its degree.

(i) $x^{5} - 2 x^{3} + x + \sqrt{3}$

(ii) $y^{3} + \sqrt{3} y$

(iii) $t^{2} - \frac{2}{5} t + \sqrt{5}$

(iv) $x^{1000} - 1$

(v) $\frac{1}{\sqrt{2}} x^{2} - \sqrt{2} x + 2$

(vi) $x^{- 2} + 2 x^{- 1} + 3$

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(viii) $\frac{- 3}{5}$

(ix) $\frac{x^{2}}{2} - \frac{2}{x^{2}}$

(x) $\sqrt[2]{2} x^{2} - 8$

(xi) $\frac{1}{2 x^{2}}$

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(xiv) $x^{4} - x^{\frac{3}{2}} + x - 3$

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x^{3} - {5 x}^{2} + 7

2 x^{3} - 7 x^{2} + 3 x + 4; 2 x^{3} - 3 x^{2} + 4 x + 1

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