Parts of a MONOMIUM

From unProfesor we bring you a new math lesson that will be very useful, especially in the study of a branch of mathematics called algebra. Specifically, we are going to see the parts of a monomial, so first we will clarify what a monomial is and, in the end, we will propose a resolved exercise so that you can verify that you have acquired the explained knowledge.

A monomial is that algebraic expression that contains literal variable unknowns (i.e. letters) and a number called coefficient. These monomials only have one term, since if there were one addition or a subtraction would be called a binomial.

So, as additions or subtractions cannot appear, since then it is not considered a monomial, can there be multiplications and powers? The answer is yes, as long as the power number is a natural number.

On the other hand, if there are several monomials adding or subtracting, we have a polynomial.

We'll see examples of each of the parts of a monomial, so that it is better understood what each of them means:

1. If we have the monomial 6x²:

• The coefficient is 6.
• The literal part is x.
• The individual degree is 2 and the absolute as well.

2. If we have the monomial 5x²and³:

• The coefficient is 5.
• The literal part is xy.
• The individual degree of x is 2 and that of y is 3. The absolute degree is 5, because 2 + 3 = 5.

3. If we have the monomial 93xy⁴z:

• The coefficient is 93.
• The literal part is xyz.
• The individual degree of x is 1, that of y is 4, and that of z is 1. The absolute degree is 6, since 1 + 4 + 1 = 6.

4. If we have the monomial -x:

• The coefficient is -1.
• The literal part is x.
• The individual degree is 1, the same as the absolute.

5. If we have the monomial xy:

• The coefficient is 1.
• The literal part is xy.
• The degree of x is 1 and the degree of y is 1. The absolute degree is 2, because 1 + 1 = 2.

To check that you have understood what has been explained throughout this lesson on monomials, we recommend that you do the proposed exercises:

1. Indicate which are the parts of the following monomials:

• x⁴
• 89x⁶and²

2. Calculate the individual degree and the absolute degree of the following monomials:

• -2x²and Z
• 8x

Then we leave you the answer to the activities raised above, so you can check if you have done them correctly:

1. Indicate which are the parts of the following monomials:

• x⁴: the coefficient is 1, the literal part is x and the degree is 4, both individual and absolute.
• 89x⁶and²: the coefficient is 89, the literal part is xy and the degree is 6 for x and 2 for y, although the absolute is 8.

2. Calculate the individual degree and the absolute degree of the following monomials:

• -2x²yz: The individual degree is 2 for x, 1 for y, and 1 for z. The absolute degree is 4.
• 8x: the individual degree is 1, the same as the absolute.

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