The degree of the polynomial $2{{x}^{2}}-4{{x}^{3}}+3x+5$ is A. 0 B. 1 C. 2 D. 3
ANSWER
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Hint: In simple words, the degree of a polynomial is the highest power that the variable has. But, the main condition is that its coefficient should be non-zero.
Complete step-by-step answer: The degree of a polynomial is the highest of the degrees of the polynomial's monomials (individual terms) with non-zero coefficients. Therefore, 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. Remember, sometimes the term order is also used in place of degree as it is its synonym. Now, let us consider the polynomial, which is given to us i.e. $2{{x}^{2}}-4{{x}^{3}}+3x+5$ The given polynomial has 4 terms. Let us consider them individually. The first term from the start is $2{{x}^{2}}$ Here, the coefficient is +2 and the power on the variable is 2. $\Rightarrow $It has a non-zero coefficient. Hence, we can consider this. The second term from the start is $-4{{x}^{3}}$ Here, the coefficient is -4 and the power on the variable is 3. $\Rightarrow $It has a non-zero coefficient. Hence, we can consider this. The third term from the start is $3x$ Here, the coefficient is +3 and the power on the variable is 1. $\Rightarrow $It has a non-zero coefficient. Hence, we can consider this. The fourth term from the start is $5$ Here, the coefficient is 5 and the power on the variable is 0. $\Rightarrow $It has a non-zero coefficient. Hence, we can consider this. Therefore, after observing the above cases, we can conclude that the highest power on the variable is 3. Hence, the degree of the given polynomial is 3.
Note: Whenever we have to determine the degree of a polynomial, always remember to first write it in the standard format. For the polynomial ${{(x+1)}^{2}}-{{(x-1)}^{2}}$ , one has to put it first in standard form by expanding the products (by using the distributive law) and then, combining the like terms.