# Algebraic degree

Introduction :

The degree of polynomial is the highest exponent for a term with non-zero coefficient in a polynomial expressed in canonical form (i.e. -as a sum or difference of terms). The degree of a term is the sum of the powers of each variable in the term. The words degree and order are used interchangeably.

Source: Wikipedia

## Algebraic degree - Example problems:

1. Find the degree of the algebraic equation

10x2+4x+12=0

Solution:

Given equation is

10x2+4x+12

The degree of the given algebraic equation is 2

2. Find the degree of the algebraic equation

11x3+5x+14

Solution:

Given equation is

11x3+5x+14

The degree of the given algebraic equation is 3

3. Find the degree of the algebraic equation

(4z9 + z5 − 4z2 + 6) + (− 4z8 + 8z4 + 2z3 + 14z)

Solution:

The given equation:

4z9+z5-4z2+6 +-4z9+8z4+2z3+14z

4z9-4z9 will be canceled

Z5-4z2+6+8z4+2z3+14z

The degree of the given algebraic equation is 5

4.  Find the degree of the algebraic equation

(5z10 + z10 − 4z2 + 6) + (5z10 + 8z10 + 2z3 + 14z)

Solution:

The given equation:

5z10+z10-4z2+6 +-5z10+8z10+2z3+14z

5z10-5z10 will be canceled

Z10-4z2+6+8z10+2z3+14z

The degree of the given algebraic equation is 10

## Algebraic degree - Example problems:

5. Find the degree of the algebraic equation

12x2+4x+12=0

Solution:

Given equation is

12x2+4x+12

The degree of the given algebraic equation is 2

6. Find the degree of the algebraic equation

(7z11 + z11 − 4z2 + 6) + (7z11 + 8z11 + 2z3 + 14z)

Solution:

The given equation:

7z11+z11-4z2+6 +-7z11+8z11+2z3+14z

7z11-7z11 will be canceled

Z11-4z2+6+8z11+2z3+14z

The degree of the given algebraic equation is 11

7. Find the degree of the algebraic equation

(8z12 + z13 − 4z2 + 6) + (8z12 + 8z4 + 2z3 + 14z)

Solution:

The given equation:

8z12+z13-4z2+6 +-8z12+8z4+2z3+14z

8z12-8z12 will be canceled

Z13-4z2+6+8z4+2z3+14z

The degree of the given algebraic equation is 13

8. Find the algebraic equation

13x2+5x+12=0

Solution:

Given equation is

13x2+5x+12

The degree of the given algebraic equation is 2

9.  Find the degree of the algebraic equation

(9z14+ z12 − 4z2 + 6) + (9z14+ 8z4 + 2z3 + 14z)

Solution:

The given equation:

9z14+z12-4z2+6 +-9z14+8z4+2z3+14z

9z14-9z14 will be canceled

Z12-4z2+6+8z4+2z3+14z

The degree of the given algebraic equation is 12