Chapter A.3, Problem 140AYU

To determine

To find: Explain why the degree of the sum of two polynomials of different degrees equals the larger of their degrees.

Answer to Problem 140AYU

1. If two polynomials have the same degree, the degree of the sum is at most this common degree.

2. If two polynomials have different degrees, the degree of the sum is the maximum of the degrees of each polynomial.

The larger Degree of any polynomial is the degree of their sum.

Suppose, $p\left(x\right)= 3x^5+2x^3 +8$; Degree: 5.

$q\left(x\right)=4x^3+4x^2+6$; degree: 3

As: $5>3$ so... degree of $p\left(x\right)+q\left(x\right)$ is: 5.

If the degree are same then degree of sum will be either that degree (coefficient same) or zero (coefficient same but diff sign) or second larger degree of any polynomial.

Explanation of Solution

1. If two polynomials have the same degree, the degree of the sum is at most this common degree.

2. If two polynomials have different degrees, the degree of the sum is the maximum of the degrees of each polynomial.

The larger Degree of any polynomial is the degree of their sum.

Suppose, $p\left(x\right)= 3x^5+2x^3 +8$; Degree: 5.

$q\left(x\right)=4x^3+4x^2+6$; degree: 3

As: $5>3$ so... degree of $p\left(x\right)+q\left(x\right)$ is: 5.

If the degree are same then degree of sum will be either that degree (coefficient same) or zero (coefficient same but diff sign) or second larger degree of any polynomial.