Question

What is the coefficient of $2x$?

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 the coefficients for the individual terms. We take arbitrary polynomials to understand the concept. Then we find the coefficient of $2x$.

Complete step by step solution:
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.
The scalar value ${{a}_{r}},r=0\left( 1 \right)n$ multiplied with every variable term with power value $r$ is considered to be the coefficient of that particular term.
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 find the coefficients of the polynomial $2x+3{{x}^{2}}+6{{x}^{7}}$.
We can write 2, 3, 6 as the coefficients of the terms \[x,{{x}^{2}},{{x}^{7}}\] respectively.
For the polynomial $2x$, the coefficient is 2.

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. There cannot be a common coefficient for the polynomial in whole even if we take a common coefficient for the polynomial.