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Write the degrees of each of the following expression:-
A. \[7{{x}^{3}}+\text{ }4{{x}^{2}}\text{- }3x\text{ }+\text{ }12\]
B. \[12\text{ }\text{- }x\text{ }+\text{ }2{{x}^{3}}\]
C. \[5y\text{ }-\sqrt{2}\]
D. 7
E. 0

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Last updated date: 13th Jun 2024
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Answer
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Hint: To find the degree of the given polynomials, let us first understand what is a degree of a polynomial. The degree of a polynomial is the largest exponent on one of its variables (for a single variable), or the largest sum of exponents on variables in a single term (for multiple variables). When there are more than one variable, we need to find the degree by adding the exponents of each variable in each term.

Complete step by step answer:
A. \[7{{x}^{3}}+\text{ }4{{x}^{2}}\text{ -}3x\text{ }+\text{ }12\]
There are four terms in this polynomial.
We can see that the degree of the first term is 3, second term is 2, third term is 1, and that of the fourth term is 0.
So, the degree of the polynomial will be ‘3’ as it is the highest degree.

B. \[12\text{ }\text{- }x\text{ }+\text{ }2{{x}^{3}}\]
There are three terms in this polynomial.
We can see that the degree of the first term is 0, second term is 1, and third term is 3.
So, the degree of the polynomial will be ‘3’ as it is the highest degree.

C. \[5y\text{ }-\sqrt{2}\]
There are only two terms in this expression. Also, we can see that there is only one variable in this whole expression, which does not have any exponent.
Since the variable ‘y’ does not have any exponent over it, therefore, its exponent must be 1.
And, as there is only one variable in the whole expression, therefore, the degree of this expression would be 1.

D. 7
There is only one term in this polynomial which is constant. Constant numbers do not have a degree.
So, the degree of the polynomial will also be ‘0’.

E. 0
There is only one term in this polynomial which is constant. Constant numbers do not have a degree.
So, the degree of the polynomial will also be ‘0’.

So, the correct answer is “Option A”.

Note: One must do all the calculations in this question very carefully. Do not get confused with the degree of a polynomial with degree of a term. Degree of a term is the highest degree associated with that term only.