Question

State whether following statement is true or false.

The degree of the sum of two polynomials each of degree $5$ is always $5.$

• A. True
• B. False

Answer 1

The correct option is B False

The degree of the sum of two polynomials each of degree $5$ is not always $5$.e.g
Let $p\left(x\right)=-3x^5+x^2+4$ and $q\left(x\right)=3x^5+x^3-1$

Clearly, both $p\left(x\right)$ and $q\left(x\right)$ are of degree $5.$

Now, $p\left(x\right)+q\left(x\right)=x^3+x^2+3$, it is polynomial of degree $3$ not $5.$

Therefore,

The degree of the sum of two polynomials each of degree $5$ is not always $5.$

option B is correct.