# Write the degree of the polynomial \[19x + \sqrt 3 x + 14\] .

Last updated date: 22nd Mar 2023

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Answer

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Hint: To find the degree of the given polynomial, represent it in the standard form and find the highest power to which the variable is raised, that is the degree of the polynomial.

Complete step-by-step answer:

A polynomial is defined as an expression that contains two or more algebraic terms. It includes constants, variables and exponents. “Poly” means many and “Nominal” means terms. Example for a polynomial is \[5{x^2} + 2\].

The polynomial is said to be in its standard form when the terms are written in the decreasing order of power. For example, the standard form of \[8x + {x^2}\] is \[{x^2} + 8x\] .

The degree of a polynomial is defined as the highest power to which the variables in the terms are raised. It is also the exponent of the first term in the standard form of the polynomial. For example, the degree of the polynomial \[{x^3} + 8x - {x^5}\] is 5.

To find the degree of the given polynomial, we first express it in the standard form. Then, we find the exponent of the variable in the first term.

Expressing the given polynomial \[19x + \sqrt 3 x + 14\] in the standard form, we get:

\[19x + \sqrt 3 x + 14 = \left( {19 + \sqrt 3 } \right)x + 14\]

The first term in the standard form is \[\left( {19 + \sqrt 3 } \right)x\]. The exponent of the variable in the first term is one.

Therefore, the degree of the polynomial is one.

Note: We can also solve by finding the exponents of all the terms of the polynomial and then choosing the highest number among them, which is also the degree of the polynomial. You might get confused with the definition of degree of polynomial as the coefficient of highest power or the exponent having the greatest coefficient, of which both are wrong.

Complete step-by-step answer:

A polynomial is defined as an expression that contains two or more algebraic terms. It includes constants, variables and exponents. “Poly” means many and “Nominal” means terms. Example for a polynomial is \[5{x^2} + 2\].

The polynomial is said to be in its standard form when the terms are written in the decreasing order of power. For example, the standard form of \[8x + {x^2}\] is \[{x^2} + 8x\] .

The degree of a polynomial is defined as the highest power to which the variables in the terms are raised. It is also the exponent of the first term in the standard form of the polynomial. For example, the degree of the polynomial \[{x^3} + 8x - {x^5}\] is 5.

To find the degree of the given polynomial, we first express it in the standard form. Then, we find the exponent of the variable in the first term.

Expressing the given polynomial \[19x + \sqrt 3 x + 14\] in the standard form, we get:

\[19x + \sqrt 3 x + 14 = \left( {19 + \sqrt 3 } \right)x + 14\]

The first term in the standard form is \[\left( {19 + \sqrt 3 } \right)x\]. The exponent of the variable in the first term is one.

Therefore, the degree of the polynomial is one.

Note: We can also solve by finding the exponents of all the terms of the polynomial and then choosing the highest number among them, which is also the degree of the polynomial. You might get confused with the definition of degree of polynomial as the coefficient of highest power or the exponent having the greatest coefficient, of which both are wrong.

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