Question

The degree of The sum of two polynomials each of degree 4is always 4? How?

Answer 1

Answer:

Because the power change only when we multiply. In addition the power do not change

Answer 2

The degree of the sum of two polynomials each of degree 4 is not always 4.

Step-by-step explanation:

Suppose two polynomials of degree 4

$p(x)=ax^4+bx^3+cx^2+dx+e$

$q(x)=-ax^4+f$

$p(x)+q(x)=ax^4+bx^3+cx^2+dx+e-ax^4+f=bx^3+cx^2+dx+e+f$

Degree of the sum of two polynomials each of degree 4=3

If suppose

$p(x)=x^4+x^3+x^2+x+1$

$q(x)=2x^4-x^3+x+1$

$p(x)+q(x)=x^4+x^3+x^2+x+1+2x^4-x^3+x+1=3x^4+x^2+2x+1$

Degree of p(x)+q(x)=4

Therefore , the degree of the sum of two polynomials each of degree 4 is not always 4.

#Learns more:

https://brainly.in/question/9352278