Question

Is the sum of two polynomials always another polynomial? if yes give an example. if no, explain

Answer 1

The sum of two polynomials is not always polynomial.

For example :

`\begin{gathered} \text{ Let, f(x)=x}^2+4x+3 \\ g(x)=x+7 \\ \text{ Sum of two polynomials} \\ f(x)+g(x)=x^2+4x+3+x+7 \\ f(x)+g(x)=x^2+5x+10 \end{gathered}`

In this sum of polynomial, the resultant is also a polynomial.

Example 2:

`\begin{gathered} \text{Let, f(x)=x}^2-7x+8 \\ g(x)=7x-x^2 \\ Add\text{ the two polynomial: f(x) + g(x)} \\ f(x)+g(x)=x^2-7x+8+7x-x^2 \\ f(x)+g(x)=8 \\ \text{ Sum of polynomial is a constant} \end{gathered}`

So, the sum of polynomial is sometime polynomial or constant.