**The Degree of Polynomials.**Notice the problem facing a researcher is designing a aluminum beam shaped container. The container should be able to accommodate 4000 ml of solution. The researcher wanted the width of the container 5 cm shorter than the length and the container height 17 cm shorter than its length. By assuming the length of the container x cm is obtained the equation x

^{3}- 22x

^{2}+ 85x - 4.000 = 0.

Can you determine the value of x that satisfies the equation?

The equation x

^{3}- 22x

^{2}+ 85x - 4.000 = 0 is a multiplying equation. This time we will discuss the matter of many tribes.

### Understanding tribes Many

Many tribes or often referred to as polynomial form tribe with a lot of values that are composed of variables and constants change. Operations used only sum, subtraction, multiplication, and rank of integers are not negative.Polynomial or multi-tribe is a form of many tribes that are finite and are composed of variables and constants. The operations that apply to the polynomial are only the sum, subtraction, multiplication, and the rank of nonnegative integers.

Inside the polynomial are known several terms such as terms, variables, coefficients, constants, and the highest rank.

Here is an explanation of these terms:

**→ f(x) = a**

_{n}x^{n}+ a_{n-1}x^{n-1}+ a_{n-2}x^{n-2}+ ..... + a_{0}The variables contained in the above polynomial are X.

The coefficients found in the above polynomials are:

a

The coefficient will always be related to its variables.

a

a

_{n}, a_{n-1}, a_{n-2}The coefficient will always be related to its variables.

a

_{n}is the coefficient of x^{n}a

_{n-1}is the coefficient of**x**and so on.^{n-1}Constants are a term that has no variables. In the above polynomial the example is

**a**. The highest rank / degree from above is if n is not equal to 0 then the polynomial is of degree n.

_{0}Some of us may think that the writing of letters will always be regarded as a variable. In a polynomial there may be two letters. When that happens, make one of these letters as coefficients or constants.

If we want to determine the degree of the polynomial, we must know the highest exponent or the degree of the polynomial. If we want to find the degree of polynomial there are several ways that can be done, namely:

**Example**

given a function x :

5x

^{2}+ 7x

^{4}- 8 + 3x + 5x

^{2}- 4x

so that we can determine the degree of polynomial in the above function, then all variables containing the same degree must be joined.

# Degree of Polynomy and Discussion

To more easily understand the above explanation just take a look at the following example:

**Problem No.1**

Arrange the 3x + x

^{4}+ 5 - 9x

^{3}polynomial in the descending rank, then declare

a. tribes and coefficients.

b. degrees and constants.

**Discussion:**

First compile the polynomial into a decreasing degrees arrangement in the absence of the missing X variable. In the above problem is not found the tribe with the variable x

^{2}, then just write the tribe as 0x

^{2}. The result is:

then, the tribes and their coefficients are:

**→**3x + x

^{4}+ 5 - 9x

^{3}

tribe x

^{4}coefficient 1

tribe -9x

^{3}coefficient -9

0x

^{2}terminology coefficient 0

3x tribe coefficient 3

5 is called a constant.

The degree of the polynomial is 4 because 4 is the highest rank of the variable. While the constant of the above polynomial is 5 because it has no variables.

**Problem No.2**

Calculate the degree of polynomial

x

^{4}+ 2x

^{3}+ 8x

**Discussion**:We use equations to determine polynomial levels. if looking for the largest exponent value the answer is 4 because it includes the largest exponent value.

**Problem No.3**

Calculate the degree of polynomial

12x

^{7}+ 3x

^{5}+ 7x + 15

**Discussion**:We use equations to determine polynomial levels. if looking for the largest exponent value the answer is 7 because it includes the largest exponent value.

**Problem No.4**

Calculate the degree of polynomial

12

^{6}+ 15x

^{5}+ 9x + 25

**Discussion:**

In the above problem, it is seen that the degree of a polynomial is 6. But the degree of polynomial applies only to the coefficient so the suitable answer is 5 because it includes the largest exponent value.

### Conclusion:

in order to complete the degree of polynomial following conclusions.1. Arrange in advance the tribe that has the greatest degree.

2. Eliminate the same tribe.

3. Calculate if the function of the equation can be completed.

So this article about "Degree of Polynomials Problems and Solving" may be useful