Question

the degree of the sum of two polynomials each of degree 5 is always 5,, true or false ​

Answer 1

Answer:

true

Explanation:

The degree of the sum of two polynomials each of degree 5 is always 5. While addition or subtraction coefficients are added and power of variables are not affected.

Answer 2

Answer:

False

Explanation:

It is not necessary that the degree of the sum of two polynomials each of degree 5 is always 5.

Let,

p(x) = $-x^{5} +x^ 2 +2$  and q(x) = $x ^5 +x ^3 +4$

p(x) and q(x) each are of degree 5.

But,

p(x) + q(x)

= $-x^ 5 +x ^2 +2+x ^5 +x^ 3 +4$

= $x ^3 +x ^2 +6$ which is not of degree 5.