Question

The degree of \[4{{x}^{3}}-12{{x}^{2}}+3x+9\] is
A. 0
B. 1
C. 2
D. 3

Answer 1

Hint: We first try to form the general form of n-degree polynomial ${{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+......+{{a}_{n}}{{x}^{n}}$. We express \[4{{x}^{3}}-12{{x}^{2}}+3x+9\] in that form to find the power value for the term with the highest value. That becomes the degree of the polynomial.

Complete step by step answer:
Any polynomial of variable $x$ can be expressed as, ${{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+......+{{a}_{n}}{{x}^{n}}$
Every term in the expression has its own power value and the maximum of those numbers defines the degree of the whole polynomial. Case in point for the above expression the height power value is $n$ and therefore, the polynomial is of n-degree.

The only term without variable $x$ is the constant term ${{a}_{0}}$. Its power value can be written as ${{a}_{0}}={{a}_{0}}{{x}^{0}}$ as ${{x}^{0}}=1$. Now we want to express the given expression \[4{{x}^{3}}-12{{x}^{2}}+3x+9\] in the form of a polynomial. The individual power values of the terms are 3, 2, 1 and 0 respectively. Maximum being 3. The maximum power value for the existing expression of \[4{{x}^{3}}-12{{x}^{2}}+3x+9\] is 3.

Hence, the correct option is D.

Note:A polynomial is the parent term used to describe a certain type of algebraic expressions that contain a certain number of monomials. We can’t take the degree of the polynomial as any power value of any monomial. It has to be the maximum one. Even if the degree is negative it has to be greater than other power values.