What is degree of polynomial ?

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What is degree of polynomial ?

What is the degree of a polynomial?

Let’s know –

The power of a polynomial is the highest power of the variable in the polynomial expression. To recall, a polynomial is defined as an expression of more than two algebraic terms, specifically the sum (or difference) of several terms having different powers of the same or different variable(s). It is a linear combination of monomials.

 For example:

\displaystyle 6{{x}^{4}}~+\text{ }2{{x}^{3}}+\text{ }3

OR,

The degree of a polynomial is defined as the highest power of

the variable of its individual terms (i.e. monomials) having non-zero coefficients.

How to find the power of a polynomial?

A polynomial is merging fixed variables with exponential powers and coefficients.

The steps to find the power of a polynomial are as follows:-

For example, if the expression is:

\displaystyle ~~5{{x}^{5}}~+\text{ }7{{x}^{3}}~+\text{ }2{{x}^{5}}+\text{ }3{{x}^{2}}+\text{ }5\text{ }+\text{ }8x\text{ }+\text{ }4

Combine all similar terms that are terms with variable terms.

\displaystyle (5{{x}^{{5~}}}+\text{ }2{{x}^{5}})\text{ }+\text{ }7{{x}^{{3~}}}+\text{ }3{{x}^{2}}+\text{ }8x\text{ }+\text{ }\left( {5\text{ }+4} \right)

then ignore all coefficients

\displaystyle {{x}^{5}}+\text{ }{{x}^{3}}+\text{ }{{x}^{2}}+\text{ }{{x}^{1}}~+\text{ }{{x}^{0}}
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Then arrange the variables in descending order of their powers

\displaystyle {{x}^{5}}+\text{ }{{x}^{3}}+\text{ }{{x}^{2}}+\text{ }{{x}^{1}}~+\text{ }{{x}^{0}}\text{ }

Then the greatest power of the variable is the power of the polynomial

Degree \displaystyle (\text{ }{{x}^{5}}+\text{ }{{x}^{3}}+\text{ }{{x}^{2}}+\text{ }{{x}^{1}}~+\text{ }{{x}^{0}})\text{ }=~\mathbf{5}5 ANSWER

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